%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : ALG136+1 : TPTP v8.1.0. Released v2.7.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n021.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 18:30:08 EDT 2022 % Result : Unsatisfiable 4.62s 4.83s % Output : Proof 4.83s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : ALG136+1 : TPTP v8.1.0. Released v2.7.0. % 0.03/0.13 % Command : run_zenon %s %d % 0.12/0.34 % Computer : n021.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Wed Jun 8 18:25:22 EDT 2022 % 0.12/0.34 % CPUTime : % 4.62/4.83 (* PROOF-FOUND *) % 4.62/4.83 % SZS status Unsatisfiable % 4.62/4.83 (* BEGIN-PROOF *) % 4.62/4.83 % SZS output start Proof % 4.62/4.83 Theorem zenon_thm : False. % 4.62/4.83 Proof. % 4.62/4.83 assert (zenon_L1_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> False). % 4.62/4.83 do 0 intro. intros zenon_H1d zenon_H1e zenon_H1f zenon_H20 zenon_H21. % 4.62/4.83 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ]. % 4.62/4.83 exact (zenon_H1e zenon_H23). % 4.62/4.83 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ]. % 4.62/4.83 exact (zenon_H1f zenon_H25). % 4.62/4.83 apply (zenon_or_s _ _ zenon_H24); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 4.62/4.83 exact (zenon_H20 zenon_H27). % 4.62/4.83 exact (zenon_H21 zenon_H26). % 4.62/4.83 (* end of lemma zenon_L1_ *) % 4.62/4.83 assert (zenon_L2_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> False). % 4.62/4.83 do 0 intro. intros zenon_H28 zenon_H29 zenon_H2a zenon_H2b zenon_H2c. % 4.62/4.83 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2e | zenon_intro zenon_H2d ]. % 4.62/4.83 exact (zenon_H29 zenon_H2e). % 4.62/4.83 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H30 | zenon_intro zenon_H2f ]. % 4.62/4.83 exact (zenon_H2a zenon_H30). % 4.62/4.83 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 4.62/4.83 exact (zenon_H2b zenon_H32). % 4.62/4.83 exact (zenon_H2c zenon_H31). % 4.62/4.83 (* end of lemma zenon_L2_ *) % 4.62/4.83 assert (zenon_L3_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 4.62/4.83 do 0 intro. intros zenon_H33 zenon_H34 zenon_H35 zenon_H36 zenon_H37 zenon_H38. % 4.62/4.83 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H3a | zenon_intro zenon_H39 ]. % 4.62/4.83 cut (((op (e1) (e0)) = (e0)) = ((op (e1) (e0)) = (op (e1) (e1)))). % 4.62/4.83 intro zenon_D_pnotp. % 4.62/4.83 apply zenon_H35. % 4.62/4.83 rewrite <- zenon_D_pnotp. % 4.62/4.83 exact zenon_H34. % 4.62/4.83 cut (((e0) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H3b]. % 4.62/4.83 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H3c]. % 4.62/4.83 congruence. % 4.62/4.83 apply zenon_H3c. apply refl_equal. % 4.62/4.83 apply zenon_H3b. apply sym_equal. exact zenon_H3a. % 4.62/4.83 apply (zenon_or_s _ _ zenon_H39); [ zenon_intro zenon_H3e | zenon_intro zenon_H3d ]. % 4.62/4.83 exact (zenon_H36 zenon_H3e). % 4.62/4.83 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H40 | zenon_intro zenon_H3f ]. % 4.62/4.83 exact (zenon_H37 zenon_H40). % 4.62/4.83 exact (zenon_H38 zenon_H3f). % 4.62/4.83 (* end of lemma zenon_L3_ *) % 4.62/4.83 assert (zenon_L4_ : (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e2) (e2)) = (e0)) -> False). % 4.62/4.83 do 0 intro. intros zenon_H41 zenon_H42 zenon_H43. % 4.62/4.83 cut (((op (e2) (e0)) = (e0)) = ((op (e2) (e0)) = (op (e2) (e2)))). % 4.62/4.83 intro zenon_D_pnotp. % 4.62/4.83 apply zenon_H41. % 4.62/4.83 rewrite <- zenon_D_pnotp. % 4.62/4.83 exact zenon_H42. % 4.62/4.83 cut (((e0) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H44]. % 4.62/4.83 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H45]. % 4.62/4.83 congruence. % 4.62/4.83 apply zenon_H45. apply refl_equal. % 4.62/4.83 apply zenon_H44. apply sym_equal. exact zenon_H43. % 4.62/4.83 (* end of lemma zenon_L4_ *) % 4.62/4.83 assert (zenon_L5_ : (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (e2)) = (e1)) -> False). % 4.62/4.83 do 0 intro. intros zenon_H46 zenon_H47 zenon_H48. % 4.62/4.83 cut (((op (e1) (e2)) = (e1)) = ((op (e1) (e2)) = (op (e2) (e2)))). % 4.62/4.83 intro zenon_D_pnotp. % 4.62/4.83 apply zenon_H46. % 4.62/4.83 rewrite <- zenon_D_pnotp. % 4.62/4.83 exact zenon_H47. % 4.62/4.83 cut (((e1) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H49]. % 4.62/4.83 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 4.62/4.83 congruence. % 4.62/4.83 apply zenon_H4a. apply refl_equal. % 4.62/4.83 apply zenon_H49. apply sym_equal. exact zenon_H48. % 4.62/4.83 (* end of lemma zenon_L5_ *) % 4.62/4.83 assert (zenon_L6_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> False). % 4.62/4.83 do 0 intro. intros zenon_H4b zenon_H42 zenon_H41 zenon_H47 zenon_H46 zenon_H4c zenon_H4d. % 4.62/4.83 apply (zenon_or_s _ _ zenon_H4b); [ zenon_intro zenon_H43 | zenon_intro zenon_H4e ]. % 4.62/4.83 apply (zenon_L4_); trivial. % 4.62/4.83 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H48 | zenon_intro zenon_H4f ]. % 4.62/4.83 apply (zenon_L5_); trivial. % 4.62/4.83 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H51 | zenon_intro zenon_H50 ]. % 4.62/4.83 exact (zenon_H4c zenon_H51). % 4.62/4.83 exact (zenon_H4d zenon_H50). % 4.62/4.83 (* end of lemma zenon_L6_ *) % 4.62/4.83 assert (zenon_L7_ : (~((e0) = (e0))) -> False). % 4.62/4.83 do 0 intro. intros zenon_H52. % 4.62/4.83 apply zenon_H52. apply refl_equal. % 4.62/4.83 (* end of lemma zenon_L7_ *) % 4.62/4.83 assert (zenon_L8_ : ((op (e2) (e0)) = (e0)) -> ((op (e2) (e0)) = (e3)) -> (~((e0) = (e3))) -> False). % 4.62/4.83 do 0 intro. intros zenon_H42 zenon_H53 zenon_H54. % 4.62/4.83 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H55 | zenon_intro zenon_H56 ]. % 4.62/4.83 cut (((e3) = (e3)) = ((e0) = (e3))). % 4.62/4.83 intro zenon_D_pnotp. % 4.62/4.83 apply zenon_H54. % 4.62/4.83 rewrite <- zenon_D_pnotp. % 4.62/4.83 exact zenon_H55. % 4.62/4.83 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H56]. % 4.62/4.83 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 4.62/4.83 congruence. % 4.62/4.83 cut (((op (e2) (e0)) = (e0)) = ((e3) = (e0))). % 4.62/4.83 intro zenon_D_pnotp. % 4.62/4.83 apply zenon_H57. % 4.62/4.83 rewrite <- zenon_D_pnotp. % 4.62/4.83 exact zenon_H42. % 4.62/4.83 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 4.62/4.83 cut (((op (e2) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 4.62/4.83 congruence. % 4.62/4.83 exact (zenon_H58 zenon_H53). % 4.62/4.83 apply zenon_H52. apply refl_equal. % 4.62/4.83 apply zenon_H56. apply refl_equal. % 4.62/4.83 apply zenon_H56. apply refl_equal. % 4.62/4.83 (* end of lemma zenon_L8_ *) % 4.62/4.83 assert (zenon_L9_ : (~((op (e0) (op (e0) (e0))) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e1)) -> False). % 4.62/4.83 do 0 intro. intros zenon_H59 zenon_H5a. % 4.62/4.83 cut (((op (e0) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H5b]. % 4.62/4.83 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 4.62/4.83 congruence. % 4.62/4.83 apply zenon_H52. apply refl_equal. % 4.62/4.83 exact (zenon_H5b zenon_H5a). % 4.62/4.83 (* end of lemma zenon_L9_ *) % 4.62/4.83 assert (zenon_L10_ : (~((e2) = (e2))) -> False). % 4.62/4.83 do 0 intro. intros zenon_H5c. % 4.62/4.83 apply zenon_H5c. apply refl_equal. % 4.62/4.83 (* end of lemma zenon_L10_ *) % 4.62/4.83 assert (zenon_L11_ : (~((e3) = (e3))) -> False). % 4.62/4.83 do 0 intro. intros zenon_H56. % 4.62/4.83 apply zenon_H56. apply refl_equal. % 4.62/4.83 (* end of lemma zenon_L11_ *) % 4.62/4.83 assert (zenon_L12_ : ((op (e2) (e1)) = (e3)) -> ((op (e0) (e1)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> False). % 4.62/4.83 do 0 intro. intros zenon_H5d zenon_H5e zenon_H5a. % 4.62/4.83 apply (zenon_notand_s _ _ ax21); [ zenon_intro zenon_H60 | zenon_intro zenon_H5f ]. % 4.62/4.83 elim (classic ((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 4.62/4.83 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0)))) = ((e2) = (op (e0) (op (e0) (e0))))). % 4.62/4.83 intro zenon_D_pnotp. % 4.62/4.83 apply zenon_H60. % 4.62/4.83 rewrite <- zenon_D_pnotp. % 4.62/4.83 exact zenon_H61. % 4.62/4.83 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 4.62/4.83 cut (((op (e0) (op (e0) (e0))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H63]. % 4.62/4.83 congruence. % 4.62/4.83 cut (((op (e0) (e1)) = (e2)) = ((op (e0) (op (e0) (e0))) = (e2))). % 4.62/4.83 intro zenon_D_pnotp. % 4.62/4.83 apply zenon_H63. % 4.62/4.83 rewrite <- zenon_D_pnotp. % 4.62/4.83 exact zenon_H5e. % 4.62/4.83 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 4.62/4.83 cut (((op (e0) (e1)) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H64]. % 4.62/4.83 congruence. % 4.62/4.83 elim (classic ((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 4.62/4.83 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0)))) = ((op (e0) (e1)) = (op (e0) (op (e0) (e0))))). % 4.62/4.83 intro zenon_D_pnotp. % 4.62/4.83 apply zenon_H64. % 4.62/4.83 rewrite <- zenon_D_pnotp. % 4.62/4.83 exact zenon_H61. % 4.62/4.83 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 4.62/4.83 cut (((op (e0) (op (e0) (e0))) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 4.62/4.83 congruence. % 4.62/4.83 apply (zenon_L9_); trivial. % 4.62/4.83 apply zenon_H62. apply refl_equal. % 4.62/4.83 apply zenon_H62. apply refl_equal. % 4.62/4.83 apply zenon_H5c. apply refl_equal. % 4.62/4.83 apply zenon_H62. apply refl_equal. % 4.62/4.83 apply zenon_H62. apply refl_equal. % 4.62/4.83 apply (zenon_notand_s _ _ zenon_H5f); [ zenon_intro zenon_H66 | zenon_intro zenon_H65 ]. % 4.62/4.83 apply zenon_H66. apply sym_equal. exact zenon_H5a. % 4.62/4.83 elim (classic ((op (op (e0) (op (e0) (e0))) (op (e0) (e0))) = (op (op (e0) (op (e0) (e0))) (op (e0) (e0))))); [ zenon_intro zenon_H67 | zenon_intro zenon_H68 ]. % 4.62/4.83 cut (((op (op (e0) (op (e0) (e0))) (op (e0) (e0))) = (op (op (e0) (op (e0) (e0))) (op (e0) (e0)))) = ((e3) = (op (op (e0) (op (e0) (e0))) (op (e0) (e0))))). % 4.62/4.83 intro zenon_D_pnotp. % 4.62/4.83 apply zenon_H65. % 4.62/4.83 rewrite <- zenon_D_pnotp. % 4.62/4.83 exact zenon_H67. % 4.62/4.83 cut (((op (op (e0) (op (e0) (e0))) (op (e0) (e0))) = (op (op (e0) (op (e0) (e0))) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H68]. % 4.62/4.83 cut (((op (op (e0) (op (e0) (e0))) (op (e0) (e0))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 4.62/4.83 congruence. % 4.62/4.83 cut (((op (e2) (e1)) = (e3)) = ((op (op (e0) (op (e0) (e0))) (op (e0) (e0))) = (e3))). % 4.62/4.83 intro zenon_D_pnotp. % 4.62/4.83 apply zenon_H69. % 4.62/4.83 rewrite <- zenon_D_pnotp. % 4.62/4.83 exact zenon_H5d. % 4.62/4.83 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H56]. % 4.62/4.83 cut (((op (e2) (e1)) = (op (op (e0) (op (e0) (e0))) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 4.62/4.83 congruence. % 4.62/4.83 elim (classic ((op (op (e0) (op (e0) (e0))) (op (e0) (e0))) = (op (op (e0) (op (e0) (e0))) (op (e0) (e0))))); [ zenon_intro zenon_H67 | zenon_intro zenon_H68 ]. % 4.62/4.83 cut (((op (op (e0) (op (e0) (e0))) (op (e0) (e0))) = (op (op (e0) (op (e0) (e0))) (op (e0) (e0)))) = ((op (e2) (e1)) = (op (op (e0) (op (e0) (e0))) (op (e0) (e0))))). % 4.62/4.83 intro zenon_D_pnotp. % 4.62/4.83 apply zenon_H6a. % 4.62/4.83 rewrite <- zenon_D_pnotp. % 4.62/4.83 exact zenon_H67. % 4.62/4.83 cut (((op (op (e0) (op (e0) (e0))) (op (e0) (e0))) = (op (op (e0) (op (e0) (e0))) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H68]. % 4.62/4.83 cut (((op (op (e0) (op (e0) (e0))) (op (e0) (e0))) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 4.62/4.83 congruence. % 4.62/4.83 cut (((op (e0) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H5b]. % 4.62/4.83 cut (((op (e0) (op (e0) (e0))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H63]. % 4.62/4.83 congruence. % 4.62/4.83 cut (((op (e0) (e1)) = (e2)) = ((op (e0) (op (e0) (e0))) = (e2))). % 4.62/4.83 intro zenon_D_pnotp. % 4.62/4.83 apply zenon_H63. % 4.62/4.83 rewrite <- zenon_D_pnotp. % 4.62/4.83 exact zenon_H5e. % 4.62/4.83 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 4.62/4.83 cut (((op (e0) (e1)) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H64]. % 4.62/4.83 congruence. % 4.62/4.83 elim (classic ((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 4.62/4.83 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0)))) = ((op (e0) (e1)) = (op (e0) (op (e0) (e0))))). % 4.62/4.83 intro zenon_D_pnotp. % 4.62/4.83 apply zenon_H64. % 4.62/4.83 rewrite <- zenon_D_pnotp. % 4.62/4.83 exact zenon_H61. % 4.62/4.83 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 4.62/4.83 cut (((op (e0) (op (e0) (e0))) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 4.62/4.83 congruence. % 4.62/4.83 apply (zenon_L9_); trivial. % 4.62/4.83 apply zenon_H62. apply refl_equal. % 4.62/4.83 apply zenon_H62. apply refl_equal. % 4.62/4.83 apply zenon_H5c. apply refl_equal. % 4.62/4.83 exact (zenon_H5b zenon_H5a). % 4.62/4.83 apply zenon_H68. apply refl_equal. % 4.62/4.83 apply zenon_H68. apply refl_equal. % 4.62/4.83 apply zenon_H56. apply refl_equal. % 4.62/4.83 apply zenon_H68. apply refl_equal. % 4.62/4.83 apply zenon_H68. apply refl_equal. % 4.62/4.83 (* end of lemma zenon_L12_ *) % 4.62/4.83 assert (zenon_L13_ : (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e3) (e3)) = (e0)) -> False). % 4.62/4.83 do 0 intro. intros zenon_H6c zenon_H26 zenon_H6d. % 4.62/4.83 cut (((op (e0) (e3)) = (e0)) = ((op (e0) (e3)) = (op (e3) (e3)))). % 4.62/4.83 intro zenon_D_pnotp. % 4.62/4.83 apply zenon_H6c. % 4.62/4.83 rewrite <- zenon_D_pnotp. % 4.62/4.83 exact zenon_H26. % 4.62/4.83 cut (((e0) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H6e]. % 4.62/4.83 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 4.62/4.83 congruence. % 4.62/4.83 apply zenon_H6f. apply refl_equal. % 4.62/4.83 apply zenon_H6e. apply sym_equal. exact zenon_H6d. % 4.62/4.83 (* end of lemma zenon_L13_ *) % 4.62/4.83 assert (zenon_L14_ : (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e3) (e3)) = (e1)) -> False). % 4.62/4.83 do 0 intro. intros zenon_H70 zenon_H71 zenon_H72. % 4.62/4.83 cut (((op (e1) (e3)) = (e1)) = ((op (e1) (e3)) = (op (e3) (e3)))). % 4.62/4.83 intro zenon_D_pnotp. % 4.62/4.83 apply zenon_H70. % 4.62/4.83 rewrite <- zenon_D_pnotp. % 4.62/4.83 exact zenon_H71. % 4.62/4.83 cut (((e1) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 4.62/4.83 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H74]. % 4.62/4.83 congruence. % 4.62/4.83 apply zenon_H74. apply refl_equal. % 4.62/4.83 apply zenon_H73. apply sym_equal. exact zenon_H72. % 4.62/4.83 (* end of lemma zenon_L14_ *) % 4.62/4.83 assert (zenon_L15_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 4.62/4.83 do 0 intro. intros zenon_H75 zenon_H26 zenon_H6c zenon_H71 zenon_H70 zenon_H76 zenon_H2c. % 4.62/4.83 apply (zenon_or_s _ _ zenon_H75); [ zenon_intro zenon_H6d | zenon_intro zenon_H77 ]. % 4.62/4.83 apply (zenon_L13_); trivial. % 4.62/4.83 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H72 | zenon_intro zenon_H78 ]. % 4.62/4.83 apply (zenon_L14_); trivial. % 4.62/4.83 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H79 | zenon_intro zenon_H31 ]. % 4.62/4.83 exact (zenon_H76 zenon_H79). % 4.62/4.83 exact (zenon_H2c zenon_H31). % 4.62/4.83 (* end of lemma zenon_L15_ *) % 4.62/4.83 assert (zenon_L16_ : (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e0)) -> ((op (e3) (e3)) = (e0)) -> False). % 4.62/4.83 do 0 intro. intros zenon_H70 zenon_H7a zenon_H6d. % 4.62/4.83 cut (((op (e1) (e3)) = (e0)) = ((op (e1) (e3)) = (op (e3) (e3)))). % 4.62/4.83 intro zenon_D_pnotp. % 4.62/4.83 apply zenon_H70. % 4.62/4.83 rewrite <- zenon_D_pnotp. % 4.62/4.83 exact zenon_H7a. % 4.62/4.83 cut (((e0) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H6e]. % 4.62/4.83 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H74]. % 4.62/4.83 congruence. % 4.62/4.83 apply zenon_H74. apply refl_equal. % 4.62/4.83 apply zenon_H6e. apply sym_equal. exact zenon_H6d. % 4.62/4.83 (* end of lemma zenon_L16_ *) % 4.62/4.83 assert (zenon_L17_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (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 (e1) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 4.62/4.83 do 0 intro. intros zenon_H7b zenon_H7c zenon_H36 zenon_H4d zenon_H4c zenon_H46 zenon_H41 zenon_H42 zenon_H4b zenon_H75 zenon_H7a zenon_H70 zenon_H76 zenon_H2c. % 4.62/4.83 apply (zenon_or_s _ _ zenon_H7b); [ zenon_intro zenon_H7e | zenon_intro zenon_H7d ]. % 4.62/4.83 exact (zenon_H7c zenon_H7e). % 4.62/4.83 apply (zenon_or_s _ _ zenon_H7d); [ zenon_intro zenon_H3e | zenon_intro zenon_H7f ]. % 4.62/4.83 exact (zenon_H36 zenon_H3e). % 4.62/4.83 apply (zenon_or_s _ _ zenon_H7f); [ zenon_intro zenon_H47 | zenon_intro zenon_H71 ]. % 4.62/4.83 apply (zenon_L6_); trivial. % 4.62/4.83 apply (zenon_or_s _ _ zenon_H75); [ zenon_intro zenon_H6d | zenon_intro zenon_H77 ]. % 4.62/4.83 apply (zenon_L16_); trivial. % 4.62/4.83 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H72 | zenon_intro zenon_H78 ]. % 4.62/4.83 apply (zenon_L14_); trivial. % 4.62/4.83 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H79 | zenon_intro zenon_H31 ]. % 4.62/4.83 exact (zenon_H76 zenon_H79). % 4.62/4.83 exact (zenon_H2c zenon_H31). % 4.62/4.83 (* end of lemma zenon_L17_ *) % 4.62/4.83 assert (zenon_L18_ : ((op (e2) (e3)) = (e0)) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> False). % 4.62/4.83 do 0 intro. intros zenon_H80 zenon_H81 zenon_H82. % 4.62/4.83 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H83 | zenon_intro zenon_H5c ]. % 4.62/4.83 cut (((e2) = (e2)) = ((e0) = (e2))). % 4.62/4.83 intro zenon_D_pnotp. % 4.62/4.83 apply zenon_H82. % 4.62/4.83 rewrite <- zenon_D_pnotp. % 4.62/4.83 exact zenon_H83. % 4.62/4.83 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 4.62/4.83 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 4.62/4.83 congruence. % 4.62/4.83 cut (((op (e2) (e3)) = (e0)) = ((e2) = (e0))). % 4.62/4.83 intro zenon_D_pnotp. % 4.62/4.83 apply zenon_H84. % 4.62/4.83 rewrite <- zenon_D_pnotp. % 4.62/4.83 exact zenon_H80. % 4.62/4.83 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 4.62/4.83 cut (((op (e2) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 4.62/4.83 congruence. % 4.62/4.83 exact (zenon_H85 zenon_H81). % 4.62/4.83 apply zenon_H52. apply refl_equal. % 4.62/4.83 apply zenon_H5c. apply refl_equal. % 4.62/4.83 apply zenon_H5c. apply refl_equal. % 4.62/4.83 (* end of lemma zenon_L18_ *) % 4.62/4.83 assert (zenon_L19_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> False). % 4.62/4.83 do 0 intro. intros zenon_H86 zenon_H87 zenon_H71. % 4.62/4.83 cut (((op (e0) (e3)) = (e1)) = ((op (e0) (e3)) = (op (e1) (e3)))). % 4.62/4.83 intro zenon_D_pnotp. % 4.62/4.83 apply zenon_H86. % 4.62/4.83 rewrite <- zenon_D_pnotp. % 4.62/4.83 exact zenon_H87. % 4.62/4.83 cut (((e1) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H88]. % 4.62/4.83 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 4.62/4.83 congruence. % 4.62/4.83 apply zenon_H6f. apply refl_equal. % 4.62/4.83 apply zenon_H88. apply sym_equal. exact zenon_H71. % 4.62/4.83 (* end of lemma zenon_L19_ *) % 4.62/4.83 assert (zenon_L20_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> False). % 4.62/4.83 do 0 intro. intros zenon_H89 zenon_H8a zenon_H81. % 4.62/4.83 cut (((op (e0) (e3)) = (e2)) = ((op (e0) (e3)) = (op (e2) (e3)))). % 4.62/4.83 intro zenon_D_pnotp. % 4.62/4.83 apply zenon_H89. % 4.62/4.83 rewrite <- zenon_D_pnotp. % 4.62/4.83 exact zenon_H8a. % 4.62/4.83 cut (((e2) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 4.62/4.83 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 4.62/4.83 congruence. % 4.62/4.83 apply zenon_H6f. apply refl_equal. % 4.62/4.83 apply zenon_H8b. apply sym_equal. exact zenon_H81. % 4.62/4.83 (* end of lemma zenon_L20_ *) % 4.62/4.83 assert (zenon_L21_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> False). % 4.62/4.83 do 0 intro. intros zenon_H89 zenon_H8c zenon_H8d. % 4.62/4.83 cut (((op (e0) (e3)) = (e3)) = ((op (e0) (e3)) = (op (e2) (e3)))). % 4.62/4.83 intro zenon_D_pnotp. % 4.62/4.83 apply zenon_H89. % 4.62/4.83 rewrite <- zenon_D_pnotp. % 4.62/4.83 exact zenon_H8c. % 4.62/4.83 cut (((e3) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H8e]. % 4.62/4.83 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 4.67/4.83 congruence. % 4.67/4.83 apply zenon_H6f. apply refl_equal. % 4.67/4.83 apply zenon_H8e. apply sym_equal. exact zenon_H8d. % 4.67/4.83 (* end of lemma zenon_L21_ *) % 4.67/4.83 assert (zenon_L22_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 4.67/4.83 do 0 intro. intros zenon_H8f zenon_H6d zenon_H6c zenon_H71 zenon_H86 zenon_H81 zenon_H89 zenon_H8d. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H26 | zenon_intro zenon_H90 ]. % 4.67/4.83 apply (zenon_L13_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H87 | zenon_intro zenon_H91 ]. % 4.67/4.83 apply (zenon_L19_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H8a | zenon_intro zenon_H8c ]. % 4.67/4.83 apply (zenon_L20_); trivial. % 4.67/4.83 apply (zenon_L21_); trivial. % 4.67/4.83 (* end of lemma zenon_L22_ *) % 4.67/4.83 assert (zenon_L23_ : ((op (e0) (e2)) = (e0)) -> ((op (e0) (e2)) = (e2)) -> (~((e0) = (e2))) -> False). % 4.67/4.83 do 0 intro. intros zenon_H27 zenon_H92 zenon_H82. % 4.67/4.83 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H83 | zenon_intro zenon_H5c ]. % 4.67/4.83 cut (((e2) = (e2)) = ((e0) = (e2))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_H82. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_H83. % 4.67/4.83 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 4.67/4.83 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 4.67/4.83 congruence. % 4.67/4.83 cut (((op (e0) (e2)) = (e0)) = ((e2) = (e0))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_H84. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_H27. % 4.67/4.83 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 4.67/4.83 cut (((op (e0) (e2)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H93]. % 4.67/4.83 congruence. % 4.67/4.83 exact (zenon_H93 zenon_H92). % 4.67/4.83 apply zenon_H52. apply refl_equal. % 4.67/4.83 apply zenon_H5c. apply refl_equal. % 4.67/4.83 apply zenon_H5c. apply refl_equal. % 4.67/4.83 (* end of lemma zenon_L23_ *) % 4.67/4.83 assert (zenon_L24_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> False). % 4.67/4.83 do 0 intro. intros zenon_H94 zenon_H95 zenon_H96 zenon_H4c zenon_H89 zenon_H8a. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H98 | zenon_intro zenon_H97 ]. % 4.67/4.83 exact (zenon_H95 zenon_H98). % 4.67/4.83 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H9a | zenon_intro zenon_H99 ]. % 4.67/4.83 exact (zenon_H96 zenon_H9a). % 4.67/4.83 apply (zenon_or_s _ _ zenon_H99); [ zenon_intro zenon_H51 | zenon_intro zenon_H81 ]. % 4.67/4.83 exact (zenon_H4c zenon_H51). % 4.67/4.83 apply (zenon_L20_); trivial. % 4.67/4.83 (* end of lemma zenon_L24_ *) % 4.67/4.83 assert (zenon_L25_ : (~((e1) = (e1))) -> False). % 4.67/4.83 do 0 intro. intros zenon_H9b. % 4.67/4.83 apply zenon_H9b. apply refl_equal. % 4.67/4.83 (* end of lemma zenon_L25_ *) % 4.67/4.83 assert (zenon_L26_ : ((op (e0) (e1)) = (e1)) -> ((op (e0) (e1)) = (e2)) -> (~((e1) = (e2))) -> False). % 4.67/4.83 do 0 intro. intros zenon_H9c zenon_H5e zenon_H9d. % 4.67/4.83 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H83 | zenon_intro zenon_H5c ]. % 4.67/4.83 cut (((e2) = (e2)) = ((e1) = (e2))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_H9d. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_H83. % 4.67/4.83 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 4.67/4.83 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9e]. % 4.67/4.83 congruence. % 4.67/4.83 cut (((op (e0) (e1)) = (e1)) = ((e2) = (e1))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_H9e. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_H9c. % 4.67/4.83 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 4.67/4.83 cut (((op (e0) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H9f]. % 4.67/4.83 congruence. % 4.67/4.83 exact (zenon_H9f zenon_H5e). % 4.67/4.83 apply zenon_H9b. apply refl_equal. % 4.67/4.83 apply zenon_H5c. apply refl_equal. % 4.67/4.83 apply zenon_H5c. apply refl_equal. % 4.67/4.83 (* end of lemma zenon_L26_ *) % 4.67/4.83 assert (zenon_L27_ : (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (e2)) = (e2)) -> False). % 4.67/4.83 do 0 intro. intros zenon_Ha0 zenon_Ha1 zenon_Ha2. % 4.67/4.83 cut (((op (e1) (e0)) = (e2)) = ((op (e1) (e0)) = (op (e1) (e2)))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_Ha0. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_Ha1. % 4.67/4.83 cut (((e2) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 4.67/4.83 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H3c]. % 4.67/4.83 congruence. % 4.67/4.83 apply zenon_H3c. apply refl_equal. % 4.67/4.83 apply zenon_Ha3. apply sym_equal. exact zenon_Ha2. % 4.67/4.83 (* end of lemma zenon_L27_ *) % 4.67/4.83 assert (zenon_L28_ : (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e2)) -> ((op (e3) (e2)) = (e2)) -> False). % 4.67/4.83 do 0 intro. intros zenon_Ha4 zenon_Ha5 zenon_Ha6. % 4.67/4.83 cut (((op (e3) (e1)) = (e2)) = ((op (e3) (e1)) = (op (e3) (e2)))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_Ha4. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_Ha5. % 4.67/4.83 cut (((e2) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Ha7]. % 4.67/4.83 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Ha8]. % 4.67/4.83 congruence. % 4.67/4.83 apply zenon_Ha8. apply refl_equal. % 4.67/4.83 apply zenon_Ha7. apply sym_equal. exact zenon_Ha6. % 4.67/4.83 (* end of lemma zenon_L28_ *) % 4.67/4.83 assert (zenon_L29_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e2)) -> False). % 4.67/4.83 do 0 intro. intros zenon_Ha9 zenon_H82 zenon_H27 zenon_Ha1 zenon_Ha0 zenon_H4c zenon_Ha4 zenon_Ha5. % 4.67/4.83 apply (zenon_or_s _ _ zenon_Ha9); [ zenon_intro zenon_H92 | zenon_intro zenon_Haa ]. % 4.67/4.83 apply (zenon_L23_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hab ]. % 4.67/4.83 apply (zenon_L27_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H51 | zenon_intro zenon_Ha6 ]. % 4.67/4.83 exact (zenon_H4c zenon_H51). % 4.67/4.83 apply (zenon_L28_); trivial. % 4.67/4.83 (* end of lemma zenon_L29_ *) % 4.67/4.83 assert (zenon_L30_ : (((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)) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 4.67/4.83 do 0 intro. intros zenon_Hac zenon_H9d zenon_H9c zenon_H37 zenon_H96 zenon_Ha9 zenon_H82 zenon_H27 zenon_Ha1 zenon_Ha0 zenon_H4c zenon_Ha4. % 4.67/4.83 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H5e | zenon_intro zenon_Had ]. % 4.67/4.83 apply (zenon_L26_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_Had); [ zenon_intro zenon_H40 | zenon_intro zenon_Hae ]. % 4.67/4.83 exact (zenon_H37 zenon_H40). % 4.67/4.83 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 4.67/4.83 exact (zenon_H96 zenon_H9a). % 4.67/4.83 apply (zenon_L29_); trivial. % 4.67/4.83 (* end of lemma zenon_L30_ *) % 4.67/4.83 assert (zenon_L31_ : ((op (e2) (e0)) = (e0)) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> False). % 4.67/4.83 do 0 intro. intros zenon_H42 zenon_H98 zenon_H82. % 4.67/4.83 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H83 | zenon_intro zenon_H5c ]. % 4.67/4.83 cut (((e2) = (e2)) = ((e0) = (e2))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_H82. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_H83. % 4.67/4.83 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 4.67/4.83 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 4.67/4.83 congruence. % 4.67/4.83 cut (((op (e2) (e0)) = (e0)) = ((e2) = (e0))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_H84. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_H42. % 4.67/4.83 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 4.67/4.83 cut (((op (e2) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H95]. % 4.67/4.83 congruence. % 4.67/4.83 exact (zenon_H95 zenon_H98). % 4.67/4.83 apply zenon_H52. apply refl_equal. % 4.67/4.83 apply zenon_H5c. apply refl_equal. % 4.67/4.83 apply zenon_H5c. apply refl_equal. % 4.67/4.83 (* end of lemma zenon_L31_ *) % 4.67/4.83 assert (zenon_L32_ : (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> False). % 4.67/4.83 do 0 intro. intros zenon_Haf zenon_Hb0 zenon_Ha5. % 4.67/4.83 cut (((op (e3) (e0)) = (e2)) = ((op (e3) (e0)) = (op (e3) (e1)))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_Haf. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_Hb0. % 4.67/4.83 cut (((e2) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hb1]. % 4.67/4.83 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 4.67/4.83 congruence. % 4.67/4.83 apply zenon_Hb2. apply refl_equal. % 4.67/4.83 apply zenon_Hb1. apply sym_equal. exact zenon_Ha5. % 4.67/4.83 (* end of lemma zenon_L32_ *) % 4.67/4.83 assert (zenon_L33_ : (((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)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e2)) -> False). % 4.67/4.83 do 0 intro. intros zenon_Hac zenon_H9d zenon_H9c zenon_H37 zenon_H96 zenon_Haf zenon_Hb0. % 4.67/4.83 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H5e | zenon_intro zenon_Had ]. % 4.67/4.83 apply (zenon_L26_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_Had); [ zenon_intro zenon_H40 | zenon_intro zenon_Hae ]. % 4.67/4.83 exact (zenon_H37 zenon_H40). % 4.67/4.83 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 4.67/4.83 exact (zenon_H96 zenon_H9a). % 4.67/4.83 apply (zenon_L32_); trivial. % 4.67/4.83 (* end of lemma zenon_L33_ *) % 4.67/4.83 assert (zenon_L34_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (((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)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 4.67/4.83 do 0 intro. intros zenon_Hb3 zenon_Hb4 zenon_Ha4 zenon_H4c zenon_Ha0 zenon_H27 zenon_Ha9 zenon_H82 zenon_H42 zenon_Hac zenon_H9d zenon_H9c zenon_H37 zenon_H96 zenon_Haf. % 4.67/4.83 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hb5 ]. % 4.67/4.83 exact (zenon_Hb4 zenon_Hb6). % 4.67/4.83 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hb7 ]. % 4.67/4.83 apply (zenon_L30_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H98 | zenon_intro zenon_Hb0 ]. % 4.67/4.83 apply (zenon_L31_); trivial. % 4.67/4.83 apply (zenon_L33_); trivial. % 4.67/4.83 (* end of lemma zenon_L34_ *) % 4.67/4.83 assert (zenon_L35_ : ((op (e0) (e2)) = (e0)) -> ((op (e0) (e2)) = (e1)) -> (~((e0) = (e1))) -> False). % 4.67/4.83 do 0 intro. intros zenon_H27 zenon_Hb8 zenon_Hb9. % 4.67/4.83 elim (classic ((e1) = (e1))); [ zenon_intro zenon_Hba | zenon_intro zenon_H9b ]. % 4.67/4.83 cut (((e1) = (e1)) = ((e0) = (e1))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_Hb9. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_Hba. % 4.67/4.83 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 4.67/4.83 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hbb]. % 4.67/4.83 congruence. % 4.67/4.83 cut (((op (e0) (e2)) = (e0)) = ((e1) = (e0))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_Hbb. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_H27. % 4.67/4.83 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 4.67/4.83 cut (((op (e0) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hbc]. % 4.67/4.83 congruence. % 4.67/4.83 exact (zenon_Hbc zenon_Hb8). % 4.67/4.83 apply zenon_H52. apply refl_equal. % 4.67/4.83 apply zenon_H9b. apply refl_equal. % 4.67/4.83 apply zenon_H9b. apply refl_equal. % 4.67/4.83 (* end of lemma zenon_L35_ *) % 4.67/4.83 assert (zenon_L36_ : ((op (e3) (e0)) = (e0)) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> False). % 4.67/4.83 do 0 intro. intros zenon_Hbd zenon_H34 zenon_Hbe. % 4.67/4.83 elim (classic ((op (e3) (e0)) = (op (e3) (e0)))); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hb2 ]. % 4.67/4.83 cut (((op (e3) (e0)) = (op (e3) (e0))) = ((op (e1) (e0)) = (op (e3) (e0)))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_Hbe. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_Hbf. % 4.67/4.83 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 4.67/4.83 cut (((op (e3) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hc0]. % 4.67/4.83 congruence. % 4.67/4.83 cut (((op (e3) (e0)) = (e0)) = ((op (e3) (e0)) = (op (e1) (e0)))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_Hc0. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_Hbd. % 4.67/4.83 cut (((e0) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hc1]. % 4.67/4.83 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 4.67/4.83 congruence. % 4.67/4.83 apply zenon_Hb2. apply refl_equal. % 4.67/4.83 apply zenon_Hc1. apply sym_equal. exact zenon_H34. % 4.67/4.83 apply zenon_Hb2. apply refl_equal. % 4.67/4.83 apply zenon_Hb2. apply refl_equal. % 4.67/4.83 (* end of lemma zenon_L36_ *) % 4.67/4.83 assert (zenon_L37_ : (~((op (e1) (op (e1) (e1))) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e0)) -> False). % 4.67/4.83 do 0 intro. intros zenon_Hc2 zenon_H3a. % 4.67/4.83 cut (((op (e1) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 4.67/4.83 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 4.67/4.83 congruence. % 4.67/4.83 apply zenon_H9b. apply refl_equal. % 4.67/4.83 exact (zenon_Hc3 zenon_H3a). % 4.67/4.83 (* end of lemma zenon_L37_ *) % 4.67/4.83 assert (zenon_L38_ : ((op (e2) (e0)) = (e3)) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> False). % 4.67/4.83 do 0 intro. intros zenon_H53 zenon_Ha1 zenon_H3a. % 4.67/4.83 apply (zenon_notand_s _ _ ax19); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hc4 ]. % 4.67/4.83 elim (classic ((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hc7 ]. % 4.67/4.83 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1)))) = ((e2) = (op (e1) (op (e1) (e1))))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_Hc5. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_Hc6. % 4.67/4.83 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_Hc7]. % 4.67/4.83 cut (((op (e1) (op (e1) (e1))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hc8]. % 4.67/4.83 congruence. % 4.67/4.83 cut (((op (e1) (e0)) = (e2)) = ((op (e1) (op (e1) (e1))) = (e2))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_Hc8. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_Ha1. % 4.67/4.83 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 4.67/4.83 cut (((op (e1) (e0)) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_Hc9]. % 4.67/4.83 congruence. % 4.67/4.83 elim (classic ((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hc7 ]. % 4.67/4.83 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1)))) = ((op (e1) (e0)) = (op (e1) (op (e1) (e1))))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_Hc9. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_Hc6. % 4.67/4.83 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_Hc7]. % 4.67/4.83 cut (((op (e1) (op (e1) (e1))) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hc2]. % 4.67/4.83 congruence. % 4.67/4.83 apply (zenon_L37_); trivial. % 4.67/4.83 apply zenon_Hc7. apply refl_equal. % 4.67/4.83 apply zenon_Hc7. apply refl_equal. % 4.67/4.83 apply zenon_H5c. apply refl_equal. % 4.67/4.83 apply zenon_Hc7. apply refl_equal. % 4.67/4.83 apply zenon_Hc7. apply refl_equal. % 4.67/4.83 apply (zenon_notand_s _ _ zenon_Hc4); [ zenon_intro zenon_H3b | zenon_intro zenon_Hca ]. % 4.67/4.83 apply zenon_H3b. apply sym_equal. exact zenon_H3a. % 4.67/4.83 elim (classic ((op (op (e1) (op (e1) (e1))) (op (e1) (e1))) = (op (op (e1) (op (e1) (e1))) (op (e1) (e1))))); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hcc ]. % 4.67/4.83 cut (((op (op (e1) (op (e1) (e1))) (op (e1) (e1))) = (op (op (e1) (op (e1) (e1))) (op (e1) (e1)))) = ((e3) = (op (op (e1) (op (e1) (e1))) (op (e1) (e1))))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_Hca. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_Hcb. % 4.67/4.83 cut (((op (op (e1) (op (e1) (e1))) (op (e1) (e1))) = (op (op (e1) (op (e1) (e1))) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_Hcc]. % 4.67/4.83 cut (((op (op (e1) (op (e1) (e1))) (op (e1) (e1))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hcd]. % 4.67/4.83 congruence. % 4.67/4.83 cut (((op (e2) (e0)) = (e3)) = ((op (op (e1) (op (e1) (e1))) (op (e1) (e1))) = (e3))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_Hcd. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_H53. % 4.67/4.83 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H56]. % 4.67/4.83 cut (((op (e2) (e0)) = (op (op (e1) (op (e1) (e1))) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_Hce]. % 4.67/4.83 congruence. % 4.67/4.83 elim (classic ((op (op (e1) (op (e1) (e1))) (op (e1) (e1))) = (op (op (e1) (op (e1) (e1))) (op (e1) (e1))))); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hcc ]. % 4.67/4.83 cut (((op (op (e1) (op (e1) (e1))) (op (e1) (e1))) = (op (op (e1) (op (e1) (e1))) (op (e1) (e1)))) = ((op (e2) (e0)) = (op (op (e1) (op (e1) (e1))) (op (e1) (e1))))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_Hce. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_Hcb. % 4.67/4.83 cut (((op (op (e1) (op (e1) (e1))) (op (e1) (e1))) = (op (op (e1) (op (e1) (e1))) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_Hcc]. % 4.67/4.83 cut (((op (op (e1) (op (e1) (e1))) (op (e1) (e1))) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hcf]. % 4.67/4.83 congruence. % 4.67/4.83 cut (((op (e1) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 4.67/4.83 cut (((op (e1) (op (e1) (e1))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hc8]. % 4.67/4.83 congruence. % 4.67/4.83 cut (((op (e1) (e0)) = (e2)) = ((op (e1) (op (e1) (e1))) = (e2))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_Hc8. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_Ha1. % 4.67/4.83 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 4.67/4.83 cut (((op (e1) (e0)) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_Hc9]. % 4.67/4.83 congruence. % 4.67/4.83 elim (classic ((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hc7 ]. % 4.67/4.83 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1)))) = ((op (e1) (e0)) = (op (e1) (op (e1) (e1))))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_Hc9. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_Hc6. % 4.67/4.83 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_Hc7]. % 4.67/4.83 cut (((op (e1) (op (e1) (e1))) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hc2]. % 4.67/4.83 congruence. % 4.67/4.83 apply (zenon_L37_); trivial. % 4.67/4.83 apply zenon_Hc7. apply refl_equal. % 4.67/4.83 apply zenon_Hc7. apply refl_equal. % 4.67/4.83 apply zenon_H5c. apply refl_equal. % 4.67/4.83 exact (zenon_Hc3 zenon_H3a). % 4.67/4.83 apply zenon_Hcc. apply refl_equal. % 4.67/4.83 apply zenon_Hcc. apply refl_equal. % 4.67/4.83 apply zenon_H56. apply refl_equal. % 4.67/4.83 apply zenon_Hcc. apply refl_equal. % 4.67/4.83 apply zenon_Hcc. apply refl_equal. % 4.67/4.83 (* end of lemma zenon_L38_ *) % 4.67/4.83 assert (zenon_L39_ : (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e3)) -> ((op (e2) (e1)) = (e3)) -> False). % 4.67/4.83 do 0 intro. intros zenon_Hd0 zenon_Hd1 zenon_H5d. % 4.67/4.83 cut (((op (e0) (e1)) = (e3)) = ((op (e0) (e1)) = (op (e2) (e1)))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_Hd0. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_Hd1. % 4.67/4.83 cut (((e3) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hd2]. % 4.67/4.83 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hd3]. % 4.67/4.83 congruence. % 4.67/4.83 apply zenon_Hd3. apply refl_equal. % 4.67/4.83 apply zenon_Hd2. apply sym_equal. exact zenon_H5d. % 4.67/4.83 (* end of lemma zenon_L39_ *) % 4.67/4.83 assert (zenon_L40_ : ((op (e0) (e3)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((e0) = (e1))) -> False). % 4.67/4.83 do 0 intro. intros zenon_H26 zenon_H87 zenon_Hb9. % 4.67/4.83 elim (classic ((e1) = (e1))); [ zenon_intro zenon_Hba | zenon_intro zenon_H9b ]. % 4.67/4.83 cut (((e1) = (e1)) = ((e0) = (e1))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_Hb9. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_Hba. % 4.67/4.83 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 4.67/4.83 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hbb]. % 4.67/4.83 congruence. % 4.67/4.83 cut (((op (e0) (e3)) = (e0)) = ((e1) = (e0))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_Hbb. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_H26. % 4.67/4.83 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 4.67/4.83 cut (((op (e0) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hd4]. % 4.67/4.83 congruence. % 4.67/4.83 exact (zenon_Hd4 zenon_H87). % 4.67/4.83 apply zenon_H52. apply refl_equal. % 4.67/4.83 apply zenon_H9b. apply refl_equal. % 4.67/4.83 apply zenon_H9b. apply refl_equal. % 4.67/4.83 (* end of lemma zenon_L40_ *) % 4.67/4.83 assert (zenon_L41_ : ((op (e2) (e3)) = (e1)) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> False). % 4.67/4.83 do 0 intro. intros zenon_Hd5 zenon_H81 zenon_H9d. % 4.67/4.83 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H83 | zenon_intro zenon_H5c ]. % 4.67/4.83 cut (((e2) = (e2)) = ((e1) = (e2))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_H9d. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_H83. % 4.67/4.83 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 4.67/4.83 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9e]. % 4.67/4.83 congruence. % 4.67/4.83 cut (((op (e2) (e3)) = (e1)) = ((e2) = (e1))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_H9e. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_Hd5. % 4.67/4.83 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 4.67/4.83 cut (((op (e2) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 4.67/4.83 congruence. % 4.67/4.83 exact (zenon_H85 zenon_H81). % 4.67/4.83 apply zenon_H9b. apply refl_equal. % 4.67/4.83 apply zenon_H5c. apply refl_equal. % 4.67/4.83 apply zenon_H5c. apply refl_equal. % 4.67/4.83 (* end of lemma zenon_L41_ *) % 4.67/4.83 assert (zenon_L42_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e1) (e3)) = (e0)) -> False). % 4.67/4.83 do 0 intro. intros zenon_H86 zenon_H26 zenon_H7a. % 4.67/4.83 cut (((op (e0) (e3)) = (e0)) = ((op (e0) (e3)) = (op (e1) (e3)))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_H86. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_H26. % 4.67/4.83 cut (((e0) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd6]. % 4.67/4.83 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 4.67/4.83 congruence. % 4.67/4.83 apply zenon_H6f. apply refl_equal. % 4.67/4.83 apply zenon_Hd6. apply sym_equal. exact zenon_H7a. % 4.67/4.83 (* end of lemma zenon_L42_ *) % 4.67/4.83 assert (zenon_L43_ : (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (e3)) = (e2)) -> False). % 4.67/4.83 do 0 intro. intros zenon_Hd7 zenon_Ha1 zenon_Hd8. % 4.67/4.83 cut (((op (e1) (e0)) = (e2)) = ((op (e1) (e0)) = (op (e1) (e3)))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_Hd7. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_Ha1. % 4.67/4.83 cut (((e2) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd9]. % 4.67/4.83 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H3c]. % 4.67/4.83 congruence. % 4.67/4.83 apply zenon_H3c. apply refl_equal. % 4.67/4.83 apply zenon_Hd9. apply sym_equal. exact zenon_Hd8. % 4.67/4.83 (* end of lemma zenon_L43_ *) % 4.67/4.83 assert (zenon_L44_ : (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> False). % 4.67/4.83 do 0 intro. intros zenon_Hda zenon_Hdb zenon_H8d. % 4.67/4.83 cut (((op (e1) (e3)) = (e3)) = ((op (e1) (e3)) = (op (e2) (e3)))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_Hda. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_Hdb. % 4.67/4.83 cut (((e3) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H8e]. % 4.67/4.83 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H74]. % 4.67/4.83 congruence. % 4.67/4.83 apply zenon_H74. apply refl_equal. % 4.67/4.83 apply zenon_H8e. apply sym_equal. exact zenon_H8d. % 4.67/4.83 (* end of lemma zenon_L44_ *) % 4.67/4.83 assert (zenon_L45_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 4.67/4.83 do 0 intro. intros zenon_Hdc zenon_H26 zenon_H86 zenon_H72 zenon_H70 zenon_Ha1 zenon_Hd7 zenon_Hda zenon_H8d. % 4.67/4.83 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H7a | zenon_intro zenon_Hdd ]. % 4.67/4.83 apply (zenon_L42_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H71 | zenon_intro zenon_Hde ]. % 4.67/4.83 apply (zenon_L14_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hdb ]. % 4.67/4.83 apply (zenon_L43_); trivial. % 4.67/4.83 apply (zenon_L44_); trivial. % 4.67/4.83 (* end of lemma zenon_L45_ *) % 4.67/4.83 assert (zenon_L46_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 4.67/4.83 do 0 intro. intros zenon_Hdf zenon_Hb9 zenon_H2c zenon_H76 zenon_H6c zenon_H75 zenon_H9d zenon_H81 zenon_Hdc zenon_H26 zenon_H86 zenon_H70 zenon_Ha1 zenon_Hd7 zenon_Hda zenon_H8d. % 4.67/4.83 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H87 | zenon_intro zenon_He0 ]. % 4.67/4.83 apply (zenon_L40_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H71 | zenon_intro zenon_He1 ]. % 4.67/4.83 apply (zenon_L15_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H72 ]. % 4.67/4.83 apply (zenon_L41_); trivial. % 4.67/4.83 apply (zenon_L45_); trivial. % 4.67/4.83 (* end of lemma zenon_L46_ *) % 4.67/4.83 assert (zenon_L47_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 4.67/4.83 do 0 intro. intros zenon_He2 zenon_H3a zenon_Hd1 zenon_Hd0 zenon_H4d zenon_Hdf zenon_Hb9 zenon_H2c zenon_H76 zenon_H6c zenon_H75 zenon_H9d zenon_H81 zenon_Hdc zenon_H26 zenon_H86 zenon_H70 zenon_Ha1 zenon_Hd7 zenon_Hda. % 4.67/4.83 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H53 | zenon_intro zenon_He3 ]. % 4.67/4.83 apply (zenon_L38_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H5d | zenon_intro zenon_He4 ]. % 4.67/4.83 apply (zenon_L39_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H50 | zenon_intro zenon_H8d ]. % 4.67/4.83 exact (zenon_H4d zenon_H50). % 4.67/4.83 apply (zenon_L46_); trivial. % 4.67/4.83 (* end of lemma zenon_L47_ *) % 4.67/4.83 assert (zenon_L48_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 4.67/4.83 do 0 intro. intros zenon_H94 zenon_H95 zenon_H96 zenon_H4c zenon_He2 zenon_H3a zenon_Hd1 zenon_Hd0 zenon_H4d zenon_Hdf zenon_Hb9 zenon_H2c zenon_H76 zenon_H6c zenon_H75 zenon_H9d zenon_Hdc zenon_H26 zenon_H86 zenon_H70 zenon_Ha1 zenon_Hd7 zenon_Hda. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H98 | zenon_intro zenon_H97 ]. % 4.67/4.83 exact (zenon_H95 zenon_H98). % 4.67/4.83 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H9a | zenon_intro zenon_H99 ]. % 4.67/4.83 exact (zenon_H96 zenon_H9a). % 4.67/4.83 apply (zenon_or_s _ _ zenon_H99); [ zenon_intro zenon_H51 | zenon_intro zenon_H81 ]. % 4.67/4.83 exact (zenon_H4c zenon_H51). % 4.67/4.83 apply (zenon_L47_); trivial. % 4.67/4.83 (* end of lemma zenon_L48_ *) % 4.67/4.83 assert (zenon_L49_ : ((op (e1) (e2)) = (e0)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> False). % 4.67/4.83 do 0 intro. intros zenon_He5 zenon_H3a zenon_He6. % 4.67/4.83 elim (classic ((op (e1) (e2)) = (op (e1) (e2)))); [ zenon_intro zenon_He7 | zenon_intro zenon_H4a ]. % 4.67/4.83 cut (((op (e1) (e2)) = (op (e1) (e2))) = ((op (e1) (e1)) = (op (e1) (e2)))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_He6. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_He7. % 4.67/4.83 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 4.67/4.83 cut (((op (e1) (e2)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_He8]. % 4.67/4.83 congruence. % 4.67/4.83 cut (((op (e1) (e2)) = (e0)) = ((op (e1) (e2)) = (op (e1) (e1)))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_He8. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_He5. % 4.67/4.83 cut (((e0) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H3b]. % 4.67/4.83 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 4.67/4.83 congruence. % 4.67/4.83 apply zenon_H4a. apply refl_equal. % 4.67/4.83 apply zenon_H3b. apply sym_equal. exact zenon_H3a. % 4.67/4.83 apply zenon_H4a. apply refl_equal. % 4.67/4.83 apply zenon_H4a. apply refl_equal. % 4.67/4.83 (* end of lemma zenon_L49_ *) % 4.67/4.83 assert (zenon_L50_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 4.67/4.83 do 0 intro. intros zenon_H33 zenon_He6 zenon_He5 zenon_H36 zenon_H37 zenon_H38. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H3a | zenon_intro zenon_H39 ]. % 4.67/4.83 apply (zenon_L49_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H39); [ zenon_intro zenon_H3e | zenon_intro zenon_H3d ]. % 4.67/4.83 exact (zenon_H36 zenon_H3e). % 4.67/4.83 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H40 | zenon_intro zenon_H3f ]. % 4.67/4.83 exact (zenon_H37 zenon_H40). % 4.67/4.83 exact (zenon_H38 zenon_H3f). % 4.67/4.83 (* end of lemma zenon_L50_ *) % 4.67/4.83 assert (zenon_L51_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 4.67/4.83 do 0 intro. intros zenon_He9 zenon_Hbe zenon_Hbd zenon_Hda zenon_Hd7 zenon_Ha1 zenon_H70 zenon_Hdc zenon_H9d zenon_H75 zenon_H6c zenon_H76 zenon_H2c zenon_Hb9 zenon_Hdf zenon_H4d zenon_Hd0 zenon_Hd1 zenon_He2 zenon_H4c zenon_H96 zenon_H95 zenon_H94 zenon_H38 zenon_H37 zenon_H36 zenon_He6 zenon_H33 zenon_H86 zenon_H26. % 4.67/4.83 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H34 | zenon_intro zenon_Hea ]. % 4.67/4.83 apply (zenon_L36_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H3a | zenon_intro zenon_Heb ]. % 4.67/4.83 apply (zenon_L48_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_He5 | zenon_intro zenon_H7a ]. % 4.67/4.83 apply (zenon_L50_); trivial. % 4.67/4.83 apply (zenon_L42_); trivial. % 4.67/4.83 (* end of lemma zenon_L51_ *) % 4.67/4.83 assert (zenon_L52_ : ((op (e1) (e0)) = (e0)) -> ((op (e1) (e0)) = (e2)) -> (~((e0) = (e2))) -> False). % 4.67/4.83 do 0 intro. intros zenon_H34 zenon_Ha1 zenon_H82. % 4.67/4.83 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H83 | zenon_intro zenon_H5c ]. % 4.67/4.83 cut (((e2) = (e2)) = ((e0) = (e2))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_H82. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_H83. % 4.67/4.83 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 4.67/4.83 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 4.67/4.83 congruence. % 4.67/4.83 cut (((op (e1) (e0)) = (e0)) = ((e2) = (e0))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_H84. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_H34. % 4.67/4.83 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 4.67/4.83 cut (((op (e1) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hec]. % 4.67/4.83 congruence. % 4.67/4.83 exact (zenon_Hec zenon_Ha1). % 4.67/4.83 apply zenon_H52. apply refl_equal. % 4.67/4.83 apply zenon_H5c. apply refl_equal. % 4.67/4.83 apply zenon_H5c. apply refl_equal. % 4.67/4.83 (* end of lemma zenon_L52_ *) % 4.67/4.83 assert (zenon_L53_ : ((op (e0) (e2)) = (e0)) -> ((op (e0) (e2)) = (e3)) -> (~((e0) = (e3))) -> False). % 4.67/4.83 do 0 intro. intros zenon_H27 zenon_Hed zenon_H54. % 4.67/4.83 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H55 | zenon_intro zenon_H56 ]. % 4.67/4.83 cut (((e3) = (e3)) = ((e0) = (e3))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_H54. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_H55. % 4.67/4.83 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H56]. % 4.67/4.83 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 4.67/4.83 congruence. % 4.67/4.83 cut (((op (e0) (e2)) = (e0)) = ((e3) = (e0))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_H57. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_H27. % 4.67/4.83 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 4.67/4.83 cut (((op (e0) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hee]. % 4.67/4.83 congruence. % 4.67/4.83 exact (zenon_Hee zenon_Hed). % 4.67/4.83 apply zenon_H52. apply refl_equal. % 4.67/4.83 apply zenon_H56. apply refl_equal. % 4.67/4.83 apply zenon_H56. apply refl_equal. % 4.67/4.83 (* end of lemma zenon_L53_ *) % 4.67/4.83 assert (zenon_L54_ : (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (e1)) = (e1)) -> False). % 4.67/4.83 do 0 intro. intros zenon_Hef zenon_Hf0 zenon_Hf1. % 4.67/4.83 cut (((op (e2) (e0)) = (e1)) = ((op (e2) (e0)) = (op (e2) (e1)))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_Hef. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_Hf0. % 4.67/4.83 cut (((e1) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hf2]. % 4.67/4.83 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H45]. % 4.67/4.83 congruence. % 4.67/4.83 apply zenon_H45. apply refl_equal. % 4.67/4.83 apply zenon_Hf2. apply sym_equal. exact zenon_Hf1. % 4.67/4.83 (* end of lemma zenon_L54_ *) % 4.67/4.83 assert (zenon_L55_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (e2))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> False). % 4.67/4.83 do 0 intro. intros zenon_Hf3 zenon_H43 zenon_H41 zenon_Hf1 zenon_Hef zenon_H95 zenon_Ha1 zenon_H3a. % 4.67/4.83 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_H42 | zenon_intro zenon_Hf4 ]. % 4.67/4.83 apply (zenon_L4_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hf5 ]. % 4.67/4.83 apply (zenon_L54_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_H98 | zenon_intro zenon_H53 ]. % 4.67/4.83 exact (zenon_H95 zenon_H98). % 4.67/4.83 apply (zenon_L38_); trivial. % 4.67/4.83 (* end of lemma zenon_L55_ *) % 4.67/4.83 assert (zenon_L56_ : (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> False). % 4.67/4.83 do 0 intro. intros zenon_Hf6 zenon_Hbd zenon_Hf7. % 4.67/4.83 cut (((op (e3) (e0)) = (e0)) = ((op (e3) (e0)) = (op (e3) (e2)))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_Hf6. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_Hbd. % 4.67/4.83 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hf8]. % 4.67/4.83 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 4.67/4.83 congruence. % 4.67/4.83 apply zenon_Hb2. apply refl_equal. % 4.67/4.83 apply zenon_Hf8. apply sym_equal. exact zenon_Hf7. % 4.67/4.83 (* end of lemma zenon_L56_ *) % 4.67/4.83 assert (zenon_L57_ : (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e3) (e3)) = (e1)) -> False). % 4.67/4.83 do 0 intro. intros zenon_Hf9 zenon_Hfa zenon_H72. % 4.67/4.83 cut (((op (e3) (e1)) = (e1)) = ((op (e3) (e1)) = (op (e3) (e3)))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_Hf9. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_Hfa. % 4.67/4.83 cut (((e1) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 4.67/4.83 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Ha8]. % 4.67/4.83 congruence. % 4.67/4.83 apply zenon_Ha8. apply refl_equal. % 4.67/4.83 apply zenon_H73. apply sym_equal. exact zenon_H72. % 4.67/4.83 (* end of lemma zenon_L57_ *) % 4.67/4.83 assert (zenon_L58_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e1)) -> False). % 4.67/4.83 do 0 intro. intros zenon_Hdf zenon_Hb9 zenon_H2c zenon_H76 zenon_H70 zenon_H6c zenon_H26 zenon_H75 zenon_H9d zenon_H81 zenon_Hf9 zenon_Hfa. % 4.67/4.83 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H87 | zenon_intro zenon_He0 ]. % 4.67/4.83 apply (zenon_L40_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H71 | zenon_intro zenon_He1 ]. % 4.67/4.83 apply (zenon_L15_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H72 ]. % 4.67/4.83 apply (zenon_L41_); trivial. % 4.67/4.83 apply (zenon_L57_); trivial. % 4.67/4.83 (* end of lemma zenon_L58_ *) % 4.67/4.83 assert (zenon_L59_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e1)) -> False). % 4.67/4.83 do 0 intro. intros zenon_H94 zenon_H95 zenon_H96 zenon_H4c zenon_Hdf zenon_Hb9 zenon_H2c zenon_H76 zenon_H70 zenon_H6c zenon_H26 zenon_H75 zenon_H9d zenon_Hf9 zenon_Hfa. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H98 | zenon_intro zenon_H97 ]. % 4.67/4.83 exact (zenon_H95 zenon_H98). % 4.67/4.83 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H9a | zenon_intro zenon_H99 ]. % 4.67/4.83 exact (zenon_H96 zenon_H9a). % 4.67/4.83 apply (zenon_or_s _ _ zenon_H99); [ zenon_intro zenon_H51 | zenon_intro zenon_H81 ]. % 4.67/4.83 exact (zenon_H4c zenon_H51). % 4.67/4.83 apply (zenon_L58_); trivial. % 4.67/4.83 (* end of lemma zenon_L59_ *) % 4.67/4.83 assert (zenon_L60_ : ((op (e0) (e3)) = (e0)) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e3))) -> False). % 4.67/4.83 do 0 intro. intros zenon_H26 zenon_H8c zenon_H54. % 4.67/4.83 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H55 | zenon_intro zenon_H56 ]. % 4.67/4.83 cut (((e3) = (e3)) = ((e0) = (e3))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_H54. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_H55. % 4.67/4.83 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H56]. % 4.67/4.83 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 4.67/4.83 congruence. % 4.67/4.83 cut (((op (e0) (e3)) = (e0)) = ((e3) = (e0))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_H57. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_H26. % 4.67/4.83 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 4.67/4.83 cut (((op (e0) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hfb]. % 4.67/4.83 congruence. % 4.67/4.83 exact (zenon_Hfb zenon_H8c). % 4.67/4.83 apply zenon_H52. apply refl_equal. % 4.67/4.83 apply zenon_H56. apply refl_equal. % 4.67/4.83 apply zenon_H56. apply refl_equal. % 4.67/4.83 (* end of lemma zenon_L60_ *) % 4.67/4.83 assert (zenon_L61_ : ((op (e3) (e0)) = (e0)) -> ((op (e3) (e0)) = (e2)) -> (~((e0) = (e2))) -> False). % 4.67/4.83 do 0 intro. intros zenon_Hbd zenon_Hb0 zenon_H82. % 4.67/4.83 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H83 | zenon_intro zenon_H5c ]. % 4.67/4.83 cut (((e2) = (e2)) = ((e0) = (e2))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_H82. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_H83. % 4.67/4.83 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 4.67/4.83 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 4.67/4.83 congruence. % 4.67/4.83 cut (((op (e3) (e0)) = (e0)) = ((e2) = (e0))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_H84. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_Hbd. % 4.67/4.83 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 4.67/4.83 cut (((op (e3) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hfc]. % 4.67/4.83 congruence. % 4.67/4.83 exact (zenon_Hfc zenon_Hb0). % 4.67/4.83 apply zenon_H52. apply refl_equal. % 4.67/4.83 apply zenon_H5c. apply refl_equal. % 4.67/4.83 apply zenon_H5c. apply refl_equal. % 4.67/4.83 (* end of lemma zenon_L61_ *) % 4.67/4.83 assert (zenon_L62_ : ((op (e0) (e2)) = (e2)) -> ((op (e0) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 4.67/4.83 do 0 intro. intros zenon_H92 zenon_Hed zenon_Hfd. % 4.67/4.83 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H55 | zenon_intro zenon_H56 ]. % 4.67/4.83 cut (((e3) = (e3)) = ((e2) = (e3))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_Hfd. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_H55. % 4.67/4.83 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H56]. % 4.67/4.83 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hfe]. % 4.67/4.83 congruence. % 4.67/4.83 cut (((op (e0) (e2)) = (e2)) = ((e3) = (e2))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_Hfe. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_H92. % 4.67/4.83 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 4.67/4.83 cut (((op (e0) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hee]. % 4.67/4.83 congruence. % 4.67/4.83 exact (zenon_Hee zenon_Hed). % 4.67/4.83 apply zenon_H5c. apply refl_equal. % 4.67/4.83 apply zenon_H56. apply refl_equal. % 4.67/4.83 apply zenon_H56. apply refl_equal. % 4.67/4.83 (* end of lemma zenon_L62_ *) % 4.67/4.83 assert (zenon_L63_ : ((op (e0) (e3)) = (e0)) -> ((op (e0) (e3)) = (e2)) -> (~((e0) = (e2))) -> False). % 4.67/4.83 do 0 intro. intros zenon_H26 zenon_H8a zenon_H82. % 4.67/4.83 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H83 | zenon_intro zenon_H5c ]. % 4.67/4.83 cut (((e2) = (e2)) = ((e0) = (e2))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_H82. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_H83. % 4.67/4.83 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 4.67/4.83 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 4.67/4.83 congruence. % 4.67/4.83 cut (((op (e0) (e3)) = (e0)) = ((e2) = (e0))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_H84. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_H26. % 4.67/4.83 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 4.67/4.83 cut (((op (e0) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hff]. % 4.67/4.83 congruence. % 4.67/4.83 exact (zenon_Hff zenon_H8a). % 4.67/4.83 apply zenon_H52. apply refl_equal. % 4.67/4.83 apply zenon_H5c. apply refl_equal. % 4.67/4.83 apply zenon_H5c. apply refl_equal. % 4.67/4.83 (* end of lemma zenon_L63_ *) % 4.67/4.83 assert (zenon_L64_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 4.67/4.83 do 0 intro. intros zenon_H100 zenon_H101 zenon_Hf6 zenon_Hf3 zenon_H41 zenon_Hef zenon_H102 zenon_Hf9 zenon_Hbd zenon_H95 zenon_H103 zenon_H104 zenon_H86 zenon_H33 zenon_He6 zenon_H36 zenon_H37 zenon_H38 zenon_H94 zenon_H96 zenon_H4c zenon_He2 zenon_Hd0 zenon_H4d zenon_Hdf zenon_Hb9 zenon_H2c zenon_H76 zenon_H6c zenon_H75 zenon_H9d zenon_Hdc zenon_H70 zenon_Hd7 zenon_Hda zenon_Hbe zenon_He9 zenon_Hfd zenon_H54 zenon_Hb4 zenon_Hb3 zenon_H26 zenon_H82. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hb6 | zenon_intro zenon_H105 ]. % 4.67/4.83 exact (zenon_Hb4 zenon_Hb6). % 4.67/4.83 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H5e | zenon_intro zenon_H106 ]. % 4.67/4.83 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hb5 ]. % 4.67/4.83 exact (zenon_Hb4 zenon_Hb6). % 4.67/4.83 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hb7 ]. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_H108 | zenon_intro zenon_H107 ]. % 4.67/4.83 exact (zenon_H104 zenon_H108). % 4.67/4.83 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H109 ]. % 4.67/4.83 apply (zenon_L51_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Hed | zenon_intro zenon_H8c ]. % 4.67/4.83 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H34 | zenon_intro zenon_Hea ]. % 4.67/4.83 apply (zenon_L52_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H3a | zenon_intro zenon_Heb ]. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H9c | zenon_intro zenon_H10a ]. % 4.67/4.83 apply (zenon_L26_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H10a); [ zenon_intro zenon_H3e | zenon_intro zenon_H10b ]. % 4.67/4.83 exact (zenon_H36 zenon_H3e). % 4.67/4.83 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hfa ]. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H27 | zenon_intro zenon_H10c ]. % 4.67/4.83 apply (zenon_L53_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_He5 | zenon_intro zenon_H10d ]. % 4.67/4.83 apply (zenon_L49_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H43 | zenon_intro zenon_Hf7 ]. % 4.67/4.83 apply (zenon_L55_); trivial. % 4.67/4.83 apply (zenon_L56_); trivial. % 4.67/4.83 apply (zenon_L59_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_He5 | zenon_intro zenon_H7a ]. % 4.67/4.83 apply (zenon_L50_); trivial. % 4.67/4.83 apply (zenon_L42_); trivial. % 4.67/4.83 apply (zenon_L60_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H98 | zenon_intro zenon_Hb0 ]. % 4.67/4.83 exact (zenon_H95 zenon_H98). % 4.67/4.83 apply (zenon_L61_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_H92 | zenon_intro zenon_H8a ]. % 4.67/4.83 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hb5 ]. % 4.67/4.83 exact (zenon_Hb4 zenon_Hb6). % 4.67/4.83 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hb7 ]. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_H108 | zenon_intro zenon_H107 ]. % 4.67/4.83 exact (zenon_H104 zenon_H108). % 4.67/4.83 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H109 ]. % 4.67/4.83 apply (zenon_L51_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Hed | zenon_intro zenon_H8c ]. % 4.67/4.83 apply (zenon_L62_); trivial. % 4.67/4.83 apply (zenon_L60_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H98 | zenon_intro zenon_Hb0 ]. % 4.67/4.83 exact (zenon_H95 zenon_H98). % 4.67/4.83 apply (zenon_L61_); trivial. % 4.67/4.83 apply (zenon_L63_); trivial. % 4.67/4.83 (* end of lemma zenon_L64_ *) % 4.67/4.83 assert (zenon_L65_ : (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> False). % 4.67/4.83 do 0 intro. intros zenon_Haf zenon_Hbd zenon_H10e. % 4.67/4.83 cut (((op (e3) (e0)) = (e0)) = ((op (e3) (e0)) = (op (e3) (e1)))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_Haf. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_Hbd. % 4.67/4.83 cut (((e0) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H10f]. % 4.67/4.83 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 4.67/4.83 congruence. % 4.67/4.83 apply zenon_Hb2. apply refl_equal. % 4.67/4.83 apply zenon_H10f. apply sym_equal. exact zenon_H10e. % 4.67/4.83 (* end of lemma zenon_L65_ *) % 4.67/4.83 assert (zenon_L66_ : (((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) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 4.67/4.83 do 0 intro. intros zenon_H75 zenon_H7a zenon_H70 zenon_Hfa zenon_Hf9 zenon_H76 zenon_H2c. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H75); [ zenon_intro zenon_H6d | zenon_intro zenon_H77 ]. % 4.67/4.83 apply (zenon_L16_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H72 | zenon_intro zenon_H78 ]. % 4.67/4.83 apply (zenon_L57_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H79 | zenon_intro zenon_H31 ]. % 4.67/4.83 exact (zenon_H76 zenon_H79). % 4.67/4.83 exact (zenon_H2c zenon_H31). % 4.67/4.83 (* end of lemma zenon_L66_ *) % 4.67/4.83 assert (zenon_L67_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> False). % 4.67/4.83 do 0 intro. intros zenon_H110 zenon_Hbd zenon_Haf zenon_H2c zenon_H76 zenon_Hf9 zenon_H70 zenon_H7a zenon_H75 zenon_Ha6 zenon_Ha4 zenon_H2a. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H110); [ zenon_intro zenon_H10e | zenon_intro zenon_H111 ]. % 4.67/4.83 apply (zenon_L65_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H111); [ zenon_intro zenon_Hfa | zenon_intro zenon_H112 ]. % 4.67/4.83 apply (zenon_L66_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H30 ]. % 4.67/4.83 apply (zenon_L28_); trivial. % 4.67/4.83 exact (zenon_H2a zenon_H30). % 4.67/4.83 (* end of lemma zenon_L67_ *) % 4.67/4.83 assert (zenon_L68_ : (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e3) (e3)) = (e0)) -> False). % 4.67/4.83 do 0 intro. intros zenon_H113 zenon_Hbd zenon_H6d. % 4.67/4.83 cut (((op (e3) (e0)) = (e0)) = ((op (e3) (e0)) = (op (e3) (e3)))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_H113. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_Hbd. % 4.67/4.83 cut (((e0) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H6e]. % 4.67/4.83 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 4.67/4.83 congruence. % 4.67/4.83 apply zenon_Hb2. apply refl_equal. % 4.67/4.83 apply zenon_H6e. apply sym_equal. exact zenon_H6d. % 4.67/4.83 (* end of lemma zenon_L68_ *) % 4.67/4.83 assert (zenon_L69_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((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 (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 4.67/4.83 do 0 intro. intros zenon_H114 zenon_H1e zenon_H35 zenon_H4b zenon_H46 zenon_H7c zenon_H7b zenon_H100 zenon_H101 zenon_Hf6 zenon_Hf3 zenon_H41 zenon_Hef zenon_H102 zenon_Hf9 zenon_H95 zenon_H103 zenon_H104 zenon_H86 zenon_H33 zenon_He6 zenon_H36 zenon_H37 zenon_H38 zenon_H94 zenon_H96 zenon_H4c zenon_He2 zenon_Hd0 zenon_H4d zenon_Hdf zenon_Hb9 zenon_H2c zenon_H76 zenon_H6c zenon_H75 zenon_H9d zenon_Hdc zenon_H70 zenon_Hd7 zenon_Hda zenon_Hbe zenon_He9 zenon_Hfd zenon_H54 zenon_Hb4 zenon_Hb3 zenon_H26 zenon_H82. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H114); [ zenon_intro zenon_H23 | zenon_intro zenon_H115 ]. % 4.67/4.83 exact (zenon_H1e zenon_H23). % 4.67/4.83 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H34 | zenon_intro zenon_H116 ]. % 4.67/4.83 apply (zenon_L3_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H42 | zenon_intro zenon_Hbd ]. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H7b); [ zenon_intro zenon_H7e | zenon_intro zenon_H7d ]. % 4.67/4.83 exact (zenon_H7c zenon_H7e). % 4.67/4.83 apply (zenon_or_s _ _ zenon_H7d); [ zenon_intro zenon_H3e | zenon_intro zenon_H7f ]. % 4.67/4.83 exact (zenon_H36 zenon_H3e). % 4.67/4.83 apply (zenon_or_s _ _ zenon_H7f); [ zenon_intro zenon_H47 | zenon_intro zenon_H71 ]. % 4.67/4.83 apply (zenon_L6_); trivial. % 4.67/4.83 apply (zenon_L15_); trivial. % 4.67/4.83 apply (zenon_L64_); trivial. % 4.67/4.83 (* end of lemma zenon_L69_ *) % 4.67/4.83 assert (zenon_L70_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((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 (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> False). % 4.67/4.83 do 0 intro. intros zenon_H1d zenon_H1f zenon_Ha9 zenon_Ha0 zenon_H117 zenon_H2a zenon_Ha4 zenon_Haf zenon_H110 zenon_H113 zenon_H118 zenon_H89 zenon_H8f zenon_Hac zenon_H114 zenon_H1e zenon_H35 zenon_H4b zenon_H46 zenon_H7c zenon_H7b zenon_H100 zenon_H101 zenon_Hf6 zenon_Hf3 zenon_H41 zenon_Hef zenon_H102 zenon_Hf9 zenon_H95 zenon_H103 zenon_H104 zenon_H86 zenon_H33 zenon_He6 zenon_H36 zenon_H37 zenon_H38 zenon_H94 zenon_H96 zenon_H4c zenon_He2 zenon_Hd0 zenon_H4d zenon_Hdf zenon_Hb9 zenon_H2c zenon_H76 zenon_H6c zenon_H75 zenon_H9d zenon_Hdc zenon_H70 zenon_Hd7 zenon_Hda zenon_Hbe zenon_He9 zenon_Hfd zenon_H54 zenon_Hb4 zenon_Hb3 zenon_H82. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ]. % 4.67/4.83 exact (zenon_H1e zenon_H23). % 4.67/4.83 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ]. % 4.67/4.83 exact (zenon_H1f zenon_H25). % 4.67/4.83 apply (zenon_or_s _ _ zenon_H24); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H114); [ zenon_intro zenon_H23 | zenon_intro zenon_H115 ]. % 4.67/4.83 exact (zenon_H1e zenon_H23). % 4.67/4.83 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H34 | zenon_intro zenon_H116 ]. % 4.67/4.83 apply (zenon_L3_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H42 | zenon_intro zenon_Hbd ]. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H5a | zenon_intro zenon_H119 ]. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hb6 | zenon_intro zenon_H105 ]. % 4.67/4.83 exact (zenon_Hb4 zenon_Hb6). % 4.67/4.83 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H5e | zenon_intro zenon_H106 ]. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H7b); [ zenon_intro zenon_H7e | zenon_intro zenon_H7d ]. % 4.67/4.83 exact (zenon_H7c zenon_H7e). % 4.67/4.83 apply (zenon_or_s _ _ zenon_H7d); [ zenon_intro zenon_H3e | zenon_intro zenon_H7f ]. % 4.67/4.83 exact (zenon_H36 zenon_H3e). % 4.67/4.83 apply (zenon_or_s _ _ zenon_H7f); [ zenon_intro zenon_H47 | zenon_intro zenon_H71 ]. % 4.67/4.83 apply (zenon_L6_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H98 | zenon_intro zenon_H97 ]. % 4.67/4.83 exact (zenon_H95 zenon_H98). % 4.67/4.83 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H9a | zenon_intro zenon_H99 ]. % 4.67/4.83 exact (zenon_H96 zenon_H9a). % 4.67/4.83 apply (zenon_or_s _ _ zenon_H99); [ zenon_intro zenon_H51 | zenon_intro zenon_H81 ]. % 4.67/4.83 exact (zenon_H4c zenon_H51). % 4.67/4.83 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H53 | zenon_intro zenon_He3 ]. % 4.67/4.83 apply (zenon_L8_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H5d | zenon_intro zenon_He4 ]. % 4.67/4.83 apply (zenon_L12_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H50 | zenon_intro zenon_H8d ]. % 4.67/4.83 exact (zenon_H4d zenon_H50). % 4.67/4.83 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H26 | zenon_intro zenon_H11a ]. % 4.67/4.83 apply (zenon_L15_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H11a); [ zenon_intro zenon_H7a | zenon_intro zenon_H11b ]. % 4.67/4.83 apply (zenon_L17_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H80 | zenon_intro zenon_H6d ]. % 4.67/4.83 apply (zenon_L18_); trivial. % 4.67/4.83 apply (zenon_L22_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_H92 | zenon_intro zenon_H8a ]. % 4.67/4.83 apply (zenon_L23_); trivial. % 4.67/4.83 apply (zenon_L24_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H9c | zenon_intro zenon_H11c ]. % 4.67/4.83 apply (zenon_L34_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H87 ]. % 4.67/4.83 apply (zenon_L35_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H7b); [ zenon_intro zenon_H7e | zenon_intro zenon_H7d ]. % 4.67/4.83 exact (zenon_H7c zenon_H7e). % 4.67/4.83 apply (zenon_or_s _ _ zenon_H7d); [ zenon_intro zenon_H3e | zenon_intro zenon_H7f ]. % 4.67/4.83 exact (zenon_H36 zenon_H3e). % 4.67/4.83 apply (zenon_or_s _ _ zenon_H7f); [ zenon_intro zenon_H47 | zenon_intro zenon_H71 ]. % 4.67/4.83 apply (zenon_L6_); trivial. % 4.67/4.83 apply (zenon_L19_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hb5 ]. % 4.67/4.83 exact (zenon_Hb4 zenon_Hb6). % 4.67/4.83 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hb7 ]. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H98 | zenon_intro zenon_H97 ]. % 4.67/4.83 exact (zenon_H95 zenon_H98). % 4.67/4.83 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H9a | zenon_intro zenon_H99 ]. % 4.67/4.83 exact (zenon_H96 zenon_H9a). % 4.67/4.83 apply (zenon_or_s _ _ zenon_H99); [ zenon_intro zenon_H51 | zenon_intro zenon_H81 ]. % 4.67/4.83 exact (zenon_H4c zenon_H51). % 4.67/4.83 apply (zenon_or_s _ _ zenon_Ha9); [ zenon_intro zenon_H92 | zenon_intro zenon_Haa ]. % 4.67/4.83 apply (zenon_L23_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hab ]. % 4.67/4.83 apply (zenon_L27_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H51 | zenon_intro zenon_Ha6 ]. % 4.67/4.83 exact (zenon_H4c zenon_H51). % 4.67/4.83 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H26 | zenon_intro zenon_H11a ]. % 4.67/4.83 apply (zenon_L64_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H11a); [ zenon_intro zenon_H7a | zenon_intro zenon_H11b ]. % 4.67/4.83 apply (zenon_L67_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H80 | zenon_intro zenon_H6d ]. % 4.67/4.83 apply (zenon_L18_); trivial. % 4.67/4.83 apply (zenon_L68_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H98 | zenon_intro zenon_Hb0 ]. % 4.67/4.83 exact (zenon_H95 zenon_H98). % 4.67/4.83 apply (zenon_L61_); trivial. % 4.67/4.83 apply (zenon_L69_); trivial. % 4.67/4.83 (* end of lemma zenon_L70_ *) % 4.67/4.83 assert (zenon_L71_ : ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (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 (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> False). % 4.67/4.83 do 0 intro. intros zenon_H11d zenon_H1e zenon_H1f zenon_H114 zenon_H113 zenon_H110 zenon_H104 zenon_He9 zenon_He6 zenon_Hdc zenon_Hda zenon_Hd7 zenon_Hdf zenon_Hd0 zenon_Hbe zenon_H102 zenon_Hf6 zenon_Hef zenon_Hf3 zenon_Hf9 zenon_H101 zenon_H103 zenon_Hfd zenon_H100 zenon_H7c zenon_H4b zenon_H4d zenon_H4c zenon_H46 zenon_H41 zenon_H94 zenon_H54 zenon_H117 zenon_H86 zenon_H89 zenon_H8f zenon_H82 zenon_H7b zenon_H6c zenon_H70 zenon_H75 zenon_He2 zenon_H96 zenon_H95 zenon_Hb4 zenon_Hb3 zenon_Haf zenon_H9d zenon_Ha9 zenon_Ha4 zenon_Ha0 zenon_Hac zenon_Hb9 zenon_H118 zenon_H35 zenon_H36 zenon_H37 zenon_H38 zenon_H33 zenon_H1d zenon_H29 zenon_H2a zenon_H2c zenon_H28. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H2b | zenon_intro zenon_H76 ]. % 4.67/4.83 apply (zenon_L2_); trivial. % 4.67/4.83 apply (zenon_L70_); trivial. % 4.67/4.83 (* end of lemma zenon_L71_ *) % 4.67/4.83 assert (zenon_L72_ : ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (((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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (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 (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> False). % 4.67/4.83 do 0 intro. intros zenon_H11e zenon_H1d zenon_H33 zenon_H38 zenon_H36 zenon_H35 zenon_H118 zenon_Hb9 zenon_Hac zenon_Ha0 zenon_Ha4 zenon_Ha9 zenon_H9d zenon_Haf zenon_Hb3 zenon_Hb4 zenon_H95 zenon_H96 zenon_He2 zenon_H75 zenon_H70 zenon_H6c zenon_H7b zenon_H82 zenon_H8f zenon_H89 zenon_H86 zenon_H117 zenon_H54 zenon_H94 zenon_H41 zenon_H46 zenon_H4c zenon_H4d zenon_H4b zenon_H7c zenon_H100 zenon_Hfd zenon_H103 zenon_H101 zenon_Hf9 zenon_Hf3 zenon_Hef zenon_Hf6 zenon_H102 zenon_Hbe zenon_Hd0 zenon_Hdf zenon_Hd7 zenon_Hda zenon_Hdc zenon_He6 zenon_He9 zenon_H104 zenon_H110 zenon_H113 zenon_H114 zenon_H1f zenon_H1e zenon_H11d zenon_H29 zenon_H2a zenon_H2c zenon_H28. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H2b | zenon_intro zenon_H37 ]. % 4.67/4.83 apply (zenon_L2_); trivial. % 4.67/4.83 apply (zenon_L71_); trivial. % 4.67/4.83 (* end of lemma zenon_L72_ *) % 4.67/4.83 assert (zenon_L73_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> False). % 4.67/4.83 do 0 intro. intros zenon_H11f zenon_H1e zenon_H5b zenon_Hb4 zenon_H104. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H23 | zenon_intro zenon_H120 ]. % 4.67/4.83 exact (zenon_H1e zenon_H23). % 4.67/4.83 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H5a | zenon_intro zenon_H121 ]. % 4.67/4.83 exact (zenon_H5b zenon_H5a). % 4.67/4.83 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_Hb6 | zenon_intro zenon_H108 ]. % 4.67/4.83 exact (zenon_Hb4 zenon_Hb6). % 4.67/4.83 exact (zenon_H104 zenon_H108). % 4.67/4.83 (* end of lemma zenon_L73_ *) % 4.67/4.83 assert (zenon_L74_ : ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 4.67/4.83 do 0 intro. intros zenon_H122 zenon_H5b zenon_Hb4 zenon_H11f zenon_H1e zenon_H1f zenon_H20 zenon_H1d. % 4.67/4.83 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_H21 | zenon_intro zenon_H104 ]. % 4.67/4.83 apply (zenon_L1_); trivial. % 4.67/4.83 apply (zenon_L73_); trivial. % 4.67/4.83 (* end of lemma zenon_L74_ *) % 4.67/4.83 assert (zenon_L75_ : ((op (e2) (e0)) = (e1)) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> False). % 4.67/4.83 do 0 intro. intros zenon_Hf0 zenon_H98 zenon_H9d. % 4.67/4.83 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H83 | zenon_intro zenon_H5c ]. % 4.67/4.83 cut (((e2) = (e2)) = ((e1) = (e2))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_H9d. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_H83. % 4.67/4.83 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 4.67/4.83 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9e]. % 4.67/4.83 congruence. % 4.67/4.83 cut (((op (e2) (e0)) = (e1)) = ((e2) = (e1))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_H9e. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_Hf0. % 4.67/4.83 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 4.67/4.83 cut (((op (e2) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H95]. % 4.67/4.83 congruence. % 4.67/4.83 exact (zenon_H95 zenon_H98). % 4.67/4.83 apply zenon_H9b. apply refl_equal. % 4.67/4.83 apply zenon_H5c. apply refl_equal. % 4.67/4.83 apply zenon_H5c. apply refl_equal. % 4.67/4.83 (* end of lemma zenon_L75_ *) % 4.67/4.83 assert (zenon_L76_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> ((op (e2) (e0)) = (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) (e1)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 4.67/4.83 do 0 intro. intros zenon_Hb3 zenon_Hb4 zenon_Ha4 zenon_H4c zenon_Ha0 zenon_H27 zenon_H82 zenon_Ha9 zenon_Hf0 zenon_Hac zenon_H9d zenon_H9c zenon_H37 zenon_H96 zenon_Haf. % 4.67/4.83 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hb5 ]. % 4.67/4.83 exact (zenon_Hb4 zenon_Hb6). % 4.67/4.83 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hb7 ]. % 4.67/4.83 apply (zenon_L30_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H98 | zenon_intro zenon_Hb0 ]. % 4.67/4.83 apply (zenon_L75_); trivial. % 4.67/4.83 apply (zenon_L33_); trivial. % 4.67/4.83 (* end of lemma zenon_L76_ *) % 4.67/4.83 assert (zenon_L77_ : ((op (e3) (e0)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> (~((e1) = (e2))) -> False). % 4.67/4.83 do 0 intro. intros zenon_H123 zenon_Hb0 zenon_H9d. % 4.67/4.83 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H83 | zenon_intro zenon_H5c ]. % 4.67/4.83 cut (((e2) = (e2)) = ((e1) = (e2))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_H9d. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_H83. % 4.67/4.83 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 4.67/4.83 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9e]. % 4.67/4.83 congruence. % 4.67/4.83 cut (((op (e3) (e0)) = (e1)) = ((e2) = (e1))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_H9e. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_H123. % 4.67/4.83 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 4.67/4.83 cut (((op (e3) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hfc]. % 4.67/4.83 congruence. % 4.67/4.83 exact (zenon_Hfc zenon_Hb0). % 4.67/4.83 apply zenon_H9b. apply refl_equal. % 4.67/4.83 apply zenon_H5c. apply refl_equal. % 4.67/4.83 apply zenon_H5c. apply refl_equal. % 4.67/4.83 (* end of lemma zenon_L77_ *) % 4.67/4.83 assert (zenon_L78_ : (((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) (e0)) = (e2))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 4.67/4.83 do 0 intro. intros zenon_Hb3 zenon_Hb4 zenon_H82 zenon_H34 zenon_H95 zenon_H123 zenon_H9d. % 4.67/4.83 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hb5 ]. % 4.67/4.83 exact (zenon_Hb4 zenon_Hb6). % 4.67/4.83 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hb7 ]. % 4.67/4.83 apply (zenon_L52_); trivial. % 4.67/4.83 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H98 | zenon_intro zenon_Hb0 ]. % 4.67/4.83 exact (zenon_H95 zenon_H98). % 4.67/4.83 apply (zenon_L77_); trivial. % 4.67/4.83 (* end of lemma zenon_L78_ *) % 4.67/4.83 assert (zenon_L79_ : ((op (e0) (e3)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> (~((e1) = (e2))) -> False). % 4.67/4.83 do 0 intro. intros zenon_H87 zenon_H8a zenon_H9d. % 4.67/4.83 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H83 | zenon_intro zenon_H5c ]. % 4.67/4.83 cut (((e2) = (e2)) = ((e1) = (e2))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_H9d. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_H83. % 4.67/4.83 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 4.67/4.83 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9e]. % 4.67/4.83 congruence. % 4.67/4.83 cut (((op (e0) (e3)) = (e1)) = ((e2) = (e1))). % 4.67/4.83 intro zenon_D_pnotp. % 4.67/4.83 apply zenon_H9e. % 4.67/4.83 rewrite <- zenon_D_pnotp. % 4.67/4.83 exact zenon_H87. % 4.67/4.83 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 4.67/4.83 cut (((op (e0) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hff]. % 4.67/4.83 congruence. % 4.67/4.83 exact (zenon_Hff zenon_H8a). % 4.67/4.83 apply zenon_H9b. apply refl_equal. % 4.67/4.83 apply zenon_H5c. apply refl_equal. % 4.67/4.83 apply zenon_H5c. apply refl_equal. % 4.67/4.84 (* end of lemma zenon_L79_ *) % 4.67/4.84 assert (zenon_L80_ : (~((op (e0) (op (e0) (e0))) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e3)) -> False). % 4.67/4.84 do 0 intro. intros zenon_H124 zenon_H108. % 4.67/4.84 cut (((op (e0) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H104]. % 4.67/4.84 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 4.67/4.84 congruence. % 4.67/4.84 apply zenon_H52. apply refl_equal. % 4.67/4.84 exact (zenon_H104 zenon_H108). % 4.67/4.84 (* end of lemma zenon_L80_ *) % 4.67/4.84 assert (zenon_L81_ : ((op (e1) (e3)) = (e2)) -> ((op (e0) (e3)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> False). % 4.67/4.84 do 0 intro. intros zenon_Hd8 zenon_H87 zenon_H108. % 4.67/4.84 apply (zenon_notand_s _ _ ax17); [ zenon_intro zenon_H126 | zenon_intro zenon_H125 ]. % 4.67/4.84 elim (classic ((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 4.67/4.84 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0)))) = ((e1) = (op (e0) (op (e0) (e0))))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_H126. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_H61. % 4.67/4.84 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 4.67/4.84 cut (((op (e0) (op (e0) (e0))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H127]. % 4.67/4.84 congruence. % 4.67/4.84 cut (((op (e0) (e3)) = (e1)) = ((op (e0) (op (e0) (e0))) = (e1))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_H127. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_H87. % 4.67/4.84 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 4.67/4.84 cut (((op (e0) (e3)) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H128]. % 4.67/4.84 congruence. % 4.67/4.84 elim (classic ((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 4.67/4.84 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0)))) = ((op (e0) (e3)) = (op (e0) (op (e0) (e0))))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_H128. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_H61. % 4.67/4.84 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 4.67/4.84 cut (((op (e0) (op (e0) (e0))) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H124]. % 4.67/4.84 congruence. % 4.67/4.84 apply (zenon_L80_); trivial. % 4.67/4.84 apply zenon_H62. apply refl_equal. % 4.67/4.84 apply zenon_H62. apply refl_equal. % 4.67/4.84 apply zenon_H9b. apply refl_equal. % 4.67/4.84 apply zenon_H62. apply refl_equal. % 4.67/4.84 apply zenon_H62. apply refl_equal. % 4.67/4.84 apply (zenon_notand_s _ _ zenon_H125); [ zenon_intro zenon_H12a | zenon_intro zenon_H129 ]. % 4.67/4.84 apply zenon_H12a. apply sym_equal. exact zenon_H108. % 4.67/4.84 elim (classic ((op (op (e0) (op (e0) (e0))) (op (e0) (e0))) = (op (op (e0) (op (e0) (e0))) (op (e0) (e0))))); [ zenon_intro zenon_H67 | zenon_intro zenon_H68 ]. % 4.67/4.84 cut (((op (op (e0) (op (e0) (e0))) (op (e0) (e0))) = (op (op (e0) (op (e0) (e0))) (op (e0) (e0)))) = ((e2) = (op (op (e0) (op (e0) (e0))) (op (e0) (e0))))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_H129. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_H67. % 4.67/4.84 cut (((op (op (e0) (op (e0) (e0))) (op (e0) (e0))) = (op (op (e0) (op (e0) (e0))) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H68]. % 4.67/4.84 cut (((op (op (e0) (op (e0) (e0))) (op (e0) (e0))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 4.67/4.84 congruence. % 4.67/4.84 cut (((op (e1) (e3)) = (e2)) = ((op (op (e0) (op (e0) (e0))) (op (e0) (e0))) = (e2))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_H12b. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_Hd8. % 4.67/4.84 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 4.67/4.84 cut (((op (e1) (e3)) = (op (op (e0) (op (e0) (e0))) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H12c]. % 4.67/4.84 congruence. % 4.67/4.84 elim (classic ((op (op (e0) (op (e0) (e0))) (op (e0) (e0))) = (op (op (e0) (op (e0) (e0))) (op (e0) (e0))))); [ zenon_intro zenon_H67 | zenon_intro zenon_H68 ]. % 4.67/4.84 cut (((op (op (e0) (op (e0) (e0))) (op (e0) (e0))) = (op (op (e0) (op (e0) (e0))) (op (e0) (e0)))) = ((op (e1) (e3)) = (op (op (e0) (op (e0) (e0))) (op (e0) (e0))))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_H12c. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_H67. % 4.67/4.84 cut (((op (op (e0) (op (e0) (e0))) (op (e0) (e0))) = (op (op (e0) (op (e0) (e0))) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H68]. % 4.67/4.84 cut (((op (op (e0) (op (e0) (e0))) (op (e0) (e0))) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12d]. % 4.67/4.84 congruence. % 4.67/4.84 cut (((op (e0) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H104]. % 4.67/4.84 cut (((op (e0) (op (e0) (e0))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H127]. % 4.67/4.84 congruence. % 4.67/4.84 cut (((op (e0) (e3)) = (e1)) = ((op (e0) (op (e0) (e0))) = (e1))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_H127. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_H87. % 4.67/4.84 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 4.67/4.84 cut (((op (e0) (e3)) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H128]. % 4.67/4.84 congruence. % 4.67/4.84 elim (classic ((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 4.67/4.84 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0)))) = ((op (e0) (e3)) = (op (e0) (op (e0) (e0))))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_H128. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_H61. % 4.67/4.84 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 4.67/4.84 cut (((op (e0) (op (e0) (e0))) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H124]. % 4.67/4.84 congruence. % 4.67/4.84 apply (zenon_L80_); trivial. % 4.67/4.84 apply zenon_H62. apply refl_equal. % 4.67/4.84 apply zenon_H62. apply refl_equal. % 4.67/4.84 apply zenon_H9b. apply refl_equal. % 4.67/4.84 exact (zenon_H104 zenon_H108). % 4.67/4.84 apply zenon_H68. apply refl_equal. % 4.67/4.84 apply zenon_H68. apply refl_equal. % 4.67/4.84 apply zenon_H5c. apply refl_equal. % 4.67/4.84 apply zenon_H68. apply refl_equal. % 4.67/4.84 apply zenon_H68. apply refl_equal. % 4.67/4.84 (* end of lemma zenon_L81_ *) % 4.67/4.84 assert (zenon_L82_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e1) (e3)) = (e2)) -> ((op (e0) (e3)) = (e1)) -> False). % 4.67/4.84 do 0 intro. intros zenon_H11f zenon_H1e zenon_H5b zenon_Hb4 zenon_Hd8 zenon_H87. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H23 | zenon_intro zenon_H120 ]. % 4.67/4.84 exact (zenon_H1e zenon_H23). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H5a | zenon_intro zenon_H121 ]. % 4.67/4.84 exact (zenon_H5b zenon_H5a). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_Hb6 | zenon_intro zenon_H108 ]. % 4.67/4.84 exact (zenon_Hb4 zenon_Hb6). % 4.67/4.84 apply (zenon_L81_); trivial. % 4.67/4.84 (* end of lemma zenon_L82_ *) % 4.67/4.84 assert (zenon_L83_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> False). % 4.67/4.84 do 0 intro. intros zenon_H12e zenon_H9d zenon_H87 zenon_Hb4 zenon_H5b zenon_H1e zenon_H11f zenon_H85 zenon_H76. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H8a | zenon_intro zenon_H12f ]. % 4.67/4.84 apply (zenon_L79_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H130 ]. % 4.67/4.84 apply (zenon_L82_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H81 | zenon_intro zenon_H79 ]. % 4.67/4.84 exact (zenon_H85 zenon_H81). % 4.67/4.84 exact (zenon_H76 zenon_H79). % 4.67/4.84 (* end of lemma zenon_L83_ *) % 4.67/4.84 assert (zenon_L84_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> False). % 4.67/4.84 do 0 intro. intros zenon_H118 zenon_Haf zenon_H96 zenon_H37 zenon_Hac zenon_H42 zenon_H82 zenon_Ha9 zenon_Ha0 zenon_H4c zenon_Ha4 zenon_Hb3 zenon_Hb9 zenon_H27 zenon_H12e zenon_H9d zenon_Hb4 zenon_H5b zenon_H1e zenon_H11f zenon_H85 zenon_H76. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H5a | zenon_intro zenon_H119 ]. % 4.67/4.84 exact (zenon_H5b zenon_H5a). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H9c | zenon_intro zenon_H11c ]. % 4.67/4.84 apply (zenon_L34_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H87 ]. % 4.67/4.84 apply (zenon_L35_); trivial. % 4.67/4.84 apply (zenon_L83_); trivial. % 4.67/4.84 (* end of lemma zenon_L84_ *) % 4.67/4.84 assert (zenon_L85_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e1)) = (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))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e1)) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> False). % 4.67/4.84 do 0 intro. intros zenon_Hb3 zenon_Hb4 zenon_Ha4 zenon_H4c zenon_Ha0 zenon_H27 zenon_Ha9 zenon_H96 zenon_H37 zenon_H9c zenon_Hac zenon_H9d zenon_Hf0 zenon_Hbd zenon_H82. % 4.67/4.84 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hb5 ]. % 4.67/4.84 exact (zenon_Hb4 zenon_Hb6). % 4.67/4.84 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hb7 ]. % 4.67/4.84 apply (zenon_L30_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H98 | zenon_intro zenon_Hb0 ]. % 4.67/4.84 apply (zenon_L75_); trivial. % 4.67/4.84 apply (zenon_L61_); trivial. % 4.67/4.84 (* end of lemma zenon_L85_ *) % 4.67/4.84 assert (zenon_L86_ : ((op (e3) (e0)) = (e0)) -> ((op (e3) (e0)) = (e1)) -> (~((e0) = (e1))) -> False). % 4.67/4.84 do 0 intro. intros zenon_Hbd zenon_H123 zenon_Hb9. % 4.67/4.84 elim (classic ((e1) = (e1))); [ zenon_intro zenon_Hba | zenon_intro zenon_H9b ]. % 4.67/4.84 cut (((e1) = (e1)) = ((e0) = (e1))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_Hb9. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_Hba. % 4.67/4.84 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 4.67/4.84 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hbb]. % 4.67/4.84 congruence. % 4.67/4.84 cut (((op (e3) (e0)) = (e0)) = ((e1) = (e0))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_Hbb. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_Hbd. % 4.67/4.84 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 4.67/4.84 cut (((op (e3) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H131]. % 4.67/4.84 congruence. % 4.67/4.84 exact (zenon_H131 zenon_H123). % 4.67/4.84 apply zenon_H52. apply refl_equal. % 4.67/4.84 apply zenon_H9b. apply refl_equal. % 4.67/4.84 apply zenon_H9b. apply refl_equal. % 4.67/4.84 (* end of lemma zenon_L86_ *) % 4.67/4.84 assert (zenon_L87_ : (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e1) (e2)) = (e1)) -> False). % 4.67/4.84 do 0 intro. intros zenon_H132 zenon_Hb8 zenon_H47. % 4.67/4.84 cut (((op (e0) (e2)) = (e1)) = ((op (e0) (e2)) = (op (e1) (e2)))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_H132. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_Hb8. % 4.67/4.84 cut (((e1) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H133]. % 4.67/4.84 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H134]. % 4.67/4.84 congruence. % 4.67/4.84 apply zenon_H134. apply refl_equal. % 4.67/4.84 apply zenon_H133. apply sym_equal. exact zenon_H47. % 4.67/4.84 (* end of lemma zenon_L87_ *) % 4.67/4.84 assert (zenon_L88_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (e1))) -> False). % 4.67/4.84 do 0 intro. intros zenon_H7b zenon_H7c zenon_H36 zenon_Hb8 zenon_H132 zenon_H135. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H7b); [ zenon_intro zenon_H7e | zenon_intro zenon_H7d ]. % 4.67/4.84 exact (zenon_H7c zenon_H7e). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H7d); [ zenon_intro zenon_H3e | zenon_intro zenon_H7f ]. % 4.67/4.84 exact (zenon_H36 zenon_H3e). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H7f); [ zenon_intro zenon_H47 | zenon_intro zenon_H71 ]. % 4.67/4.84 apply (zenon_L87_); trivial. % 4.67/4.84 exact (zenon_H135 zenon_H71). % 4.67/4.84 (* end of lemma zenon_L88_ *) % 4.67/4.84 assert (zenon_L89_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> False). % 4.67/4.84 do 0 intro. intros zenon_H94 zenon_H95 zenon_H5e zenon_Hd0 zenon_H4c zenon_H85. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H98 | zenon_intro zenon_H97 ]. % 4.67/4.84 exact (zenon_H95 zenon_H98). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H9a | zenon_intro zenon_H99 ]. % 4.67/4.84 cut (((op (e0) (e1)) = (e2)) = ((op (e0) (e1)) = (op (e2) (e1)))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_Hd0. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_H5e. % 4.67/4.84 cut (((e2) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H136]. % 4.67/4.84 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hd3]. % 4.67/4.84 congruence. % 4.67/4.84 apply zenon_Hd3. apply refl_equal. % 4.67/4.84 apply zenon_H136. apply sym_equal. exact zenon_H9a. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H99); [ zenon_intro zenon_H51 | zenon_intro zenon_H81 ]. % 4.67/4.84 exact (zenon_H4c zenon_H51). % 4.67/4.84 exact (zenon_H85 zenon_H81). % 4.67/4.84 (* end of lemma zenon_L89_ *) % 4.67/4.84 assert (zenon_L90_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 4.67/4.84 do 0 intro. intros zenon_H100 zenon_Hb4 zenon_H85 zenon_H4c zenon_Hd0 zenon_H95 zenon_H94 zenon_H82 zenon_H27 zenon_H87 zenon_H9d. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hb6 | zenon_intro zenon_H105 ]. % 4.67/4.84 exact (zenon_Hb4 zenon_Hb6). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H5e | zenon_intro zenon_H106 ]. % 4.67/4.84 apply (zenon_L89_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_H92 | zenon_intro zenon_H8a ]. % 4.67/4.84 apply (zenon_L23_); trivial. % 4.67/4.84 apply (zenon_L79_); trivial. % 4.67/4.84 (* end of lemma zenon_L90_ *) % 4.67/4.84 assert (zenon_L91_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> False). % 4.67/4.84 do 0 intro. intros zenon_H1d zenon_H1f zenon_H9d zenon_H82 zenon_H94 zenon_H95 zenon_Hd0 zenon_H4c zenon_H85 zenon_Hb4 zenon_H100 zenon_H7b zenon_H7c zenon_H36 zenon_H132 zenon_H135 zenon_H137 zenon_H5b zenon_Hac zenon_H37 zenon_H96 zenon_Ha9 zenon_Ha0 zenon_Ha4 zenon_Hb3 zenon_Hb9 zenon_H118 zenon_Haf zenon_H12e zenon_H1e zenon_H11f zenon_H76 zenon_H114 zenon_H21. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ]. % 4.67/4.84 exact (zenon_H1e zenon_H23). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ]. % 4.67/4.84 exact (zenon_H1f zenon_H25). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H24); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H114); [ zenon_intro zenon_H23 | zenon_intro zenon_H115 ]. % 4.67/4.84 exact (zenon_H1e zenon_H23). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H34 | zenon_intro zenon_H116 ]. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H5a | zenon_intro zenon_H119 ]. % 4.67/4.84 exact (zenon_H5b zenon_H5a). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H9c | zenon_intro zenon_H11c ]. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_H5a | zenon_intro zenon_H138 ]. % 4.67/4.84 exact (zenon_H5b zenon_H5a). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_H7e | zenon_intro zenon_H139 ]. % 4.67/4.84 exact (zenon_H7c zenon_H7e). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H123 ]. % 4.67/4.84 apply (zenon_L76_); trivial. % 4.67/4.84 apply (zenon_L78_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H87 ]. % 4.67/4.84 apply (zenon_L35_); trivial. % 4.67/4.84 apply (zenon_L83_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H42 | zenon_intro zenon_Hbd ]. % 4.67/4.84 apply (zenon_L84_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H5a | zenon_intro zenon_H119 ]. % 4.67/4.84 exact (zenon_H5b zenon_H5a). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H9c | zenon_intro zenon_H11c ]. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_H5a | zenon_intro zenon_H138 ]. % 4.67/4.84 exact (zenon_H5b zenon_H5a). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_H7e | zenon_intro zenon_H139 ]. % 4.67/4.84 exact (zenon_H7c zenon_H7e). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H123 ]. % 4.67/4.84 apply (zenon_L85_); trivial. % 4.67/4.84 apply (zenon_L86_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H87 ]. % 4.67/4.84 apply (zenon_L88_); trivial. % 4.67/4.84 apply (zenon_L90_); trivial. % 4.67/4.84 exact (zenon_H21 zenon_H26). % 4.67/4.84 (* end of lemma zenon_L91_ *) % 4.67/4.84 assert (zenon_L92_ : ((op (e0) (e1)) = (e0)) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e1))) -> False). % 4.67/4.84 do 0 intro. intros zenon_H25 zenon_H9c zenon_Hb9. % 4.67/4.84 elim (classic ((e1) = (e1))); [ zenon_intro zenon_Hba | zenon_intro zenon_H9b ]. % 4.67/4.84 cut (((e1) = (e1)) = ((e0) = (e1))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_Hb9. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_Hba. % 4.67/4.84 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 4.67/4.84 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hbb]. % 4.67/4.84 congruence. % 4.67/4.84 cut (((op (e0) (e1)) = (e0)) = ((e1) = (e0))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_Hbb. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_H25. % 4.67/4.84 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 4.67/4.84 cut (((op (e0) (e1)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H13a]. % 4.67/4.84 congruence. % 4.67/4.84 exact (zenon_H13a zenon_H9c). % 4.67/4.84 apply zenon_H52. apply refl_equal. % 4.67/4.84 apply zenon_H9b. apply refl_equal. % 4.67/4.84 apply zenon_H9b. apply refl_equal. % 4.67/4.84 (* end of lemma zenon_L92_ *) % 4.67/4.84 assert (zenon_L93_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e3)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> False). % 4.67/4.84 do 0 intro. intros zenon_H12e zenon_H9d zenon_H108 zenon_H87 zenon_H85 zenon_H76. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H8a | zenon_intro zenon_H12f ]. % 4.67/4.84 apply (zenon_L79_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H130 ]. % 4.67/4.84 apply (zenon_L81_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H81 | zenon_intro zenon_H79 ]. % 4.67/4.84 exact (zenon_H85 zenon_H81). % 4.67/4.84 exact (zenon_H76 zenon_H79). % 4.67/4.84 (* end of lemma zenon_L93_ *) % 4.67/4.84 assert (zenon_L94_ : ((op (e0) (e1)) = (e0)) -> ((op (e0) (e1)) = (e3)) -> (~((e0) = (e3))) -> False). % 4.67/4.84 do 0 intro. intros zenon_H25 zenon_Hd1 zenon_H54. % 4.67/4.84 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H55 | zenon_intro zenon_H56 ]. % 4.67/4.84 cut (((e3) = (e3)) = ((e0) = (e3))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_H54. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_H55. % 4.67/4.84 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H56]. % 4.67/4.84 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 4.67/4.84 congruence. % 4.67/4.84 cut (((op (e0) (e1)) = (e0)) = ((e3) = (e0))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_H57. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_H25. % 4.67/4.84 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 4.67/4.84 cut (((op (e0) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H13b]. % 4.67/4.84 congruence. % 4.67/4.84 exact (zenon_H13b zenon_Hd1). % 4.67/4.84 apply zenon_H52. apply refl_equal. % 4.67/4.84 apply zenon_H56. apply refl_equal. % 4.67/4.84 apply zenon_H56. apply refl_equal. % 4.67/4.84 (* end of lemma zenon_L94_ *) % 4.67/4.84 assert (zenon_L95_ : ((op (e0) (e3)) = (e1)) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e3))) -> False). % 4.67/4.84 do 0 intro. intros zenon_H87 zenon_H8c zenon_H13c. % 4.67/4.84 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H55 | zenon_intro zenon_H56 ]. % 4.67/4.84 cut (((e3) = (e3)) = ((e1) = (e3))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_H13c. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_H55. % 4.67/4.84 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H56]. % 4.67/4.84 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H13d]. % 4.67/4.84 congruence. % 4.67/4.84 cut (((op (e0) (e3)) = (e1)) = ((e3) = (e1))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_H13d. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_H87. % 4.67/4.84 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 4.67/4.84 cut (((op (e0) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hfb]. % 4.67/4.84 congruence. % 4.67/4.84 exact (zenon_Hfb zenon_H8c). % 4.67/4.84 apply zenon_H9b. apply refl_equal. % 4.67/4.84 apply zenon_H56. apply refl_equal. % 4.67/4.84 apply zenon_H56. apply refl_equal. % 4.67/4.84 (* end of lemma zenon_L95_ *) % 4.67/4.84 assert (zenon_L96_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> False). % 4.67/4.84 do 0 intro. intros zenon_H118 zenon_H5b zenon_Hb9 zenon_H135 zenon_H132 zenon_H36 zenon_H7c zenon_H7b zenon_H100 zenon_Hb4 zenon_H4c zenon_Hd0 zenon_H95 zenon_H94 zenon_H13c zenon_Hfd zenon_H25 zenon_H54 zenon_H12e zenon_H85 zenon_H76 zenon_H103 zenon_H9d. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H5a | zenon_intro zenon_H119 ]. % 4.67/4.84 exact (zenon_H5b zenon_H5a). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H9c | zenon_intro zenon_H11c ]. % 4.67/4.84 apply (zenon_L92_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H87 ]. % 4.67/4.84 apply (zenon_L88_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hb6 | zenon_intro zenon_H105 ]. % 4.67/4.84 exact (zenon_Hb4 zenon_Hb6). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H5e | zenon_intro zenon_H106 ]. % 4.67/4.84 apply (zenon_L89_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_H92 | zenon_intro zenon_H8a ]. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_H108 | zenon_intro zenon_H107 ]. % 4.67/4.84 apply (zenon_L93_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H109 ]. % 4.67/4.84 apply (zenon_L94_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Hed | zenon_intro zenon_H8c ]. % 4.67/4.84 apply (zenon_L62_); trivial. % 4.67/4.84 apply (zenon_L95_); trivial. % 4.67/4.84 apply (zenon_L79_); trivial. % 4.67/4.84 (* end of lemma zenon_L96_ *) % 4.67/4.84 assert (zenon_L97_ : (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (e3)) = (e1)) -> False). % 4.67/4.84 do 0 intro. intros zenon_H13e zenon_Hf0 zenon_Hd5. % 4.67/4.84 cut (((op (e2) (e0)) = (e1)) = ((op (e2) (e0)) = (op (e2) (e3)))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_H13e. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_Hf0. % 4.67/4.84 cut (((e1) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H13f]. % 4.67/4.84 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H45]. % 4.67/4.84 congruence. % 4.67/4.84 apply zenon_H45. apply refl_equal. % 4.67/4.84 apply zenon_H13f. apply sym_equal. exact zenon_Hd5. % 4.67/4.84 (* end of lemma zenon_L97_ *) % 4.67/4.84 assert (zenon_L98_ : (((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)) = (e1))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 4.67/4.84 do 0 intro. intros zenon_Hdf zenon_H9d zenon_H8a zenon_H135 zenon_Hf0 zenon_H13e zenon_H140. % 4.67/4.84 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H87 | zenon_intro zenon_He0 ]. % 4.67/4.84 apply (zenon_L79_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H71 | zenon_intro zenon_He1 ]. % 4.67/4.84 exact (zenon_H135 zenon_H71). % 4.67/4.84 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H72 ]. % 4.67/4.84 apply (zenon_L97_); trivial. % 4.67/4.84 exact (zenon_H140 zenon_H72). % 4.67/4.84 (* end of lemma zenon_L98_ *) % 4.67/4.84 assert (zenon_L99_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e2) (e0)) = (e2))) -> (~((e1) = (e2))) -> False). % 4.67/4.84 do 0 intro. intros zenon_H137 zenon_H5b zenon_H7c zenon_H140 zenon_H13e zenon_H135 zenon_Hdf zenon_H27 zenon_H94 zenon_Hd0 zenon_H4c zenon_H85 zenon_H100 zenon_Hb3 zenon_Hb4 zenon_H82 zenon_H34 zenon_H95 zenon_H9d. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_H5a | zenon_intro zenon_H138 ]. % 4.67/4.84 exact (zenon_H5b zenon_H5a). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_H7e | zenon_intro zenon_H139 ]. % 4.67/4.84 exact (zenon_H7c zenon_H7e). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H123 ]. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hb6 | zenon_intro zenon_H105 ]. % 4.67/4.84 exact (zenon_Hb4 zenon_Hb6). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H5e | zenon_intro zenon_H106 ]. % 4.67/4.84 apply (zenon_L89_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_H92 | zenon_intro zenon_H8a ]. % 4.67/4.84 apply (zenon_L23_); trivial. % 4.67/4.84 apply (zenon_L98_); trivial. % 4.67/4.84 apply (zenon_L78_); trivial. % 4.67/4.84 (* end of lemma zenon_L99_ *) % 4.67/4.84 assert (zenon_L100_ : ((op (e2) (e0)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> (~((e0) = (e1))) -> False). % 4.67/4.84 do 0 intro. intros zenon_H42 zenon_Hf0 zenon_Hb9. % 4.67/4.84 elim (classic ((e1) = (e1))); [ zenon_intro zenon_Hba | zenon_intro zenon_H9b ]. % 4.67/4.84 cut (((e1) = (e1)) = ((e0) = (e1))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_Hb9. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_Hba. % 4.67/4.84 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 4.67/4.84 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hbb]. % 4.67/4.84 congruence. % 4.67/4.84 cut (((op (e2) (e0)) = (e0)) = ((e1) = (e0))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_Hbb. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_H42. % 4.67/4.84 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 4.67/4.84 cut (((op (e2) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H141]. % 4.67/4.84 congruence. % 4.67/4.84 exact (zenon_H141 zenon_Hf0). % 4.67/4.84 apply zenon_H52. apply refl_equal. % 4.67/4.84 apply zenon_H9b. apply refl_equal. % 4.67/4.84 apply zenon_H9b. apply refl_equal. % 4.67/4.84 (* end of lemma zenon_L100_ *) % 4.67/4.84 assert (zenon_L101_ : (((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). % 4.67/4.84 do 0 intro. intros zenon_H75 zenon_H7a zenon_H70 zenon_H140 zenon_H76 zenon_H2c. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H75); [ zenon_intro zenon_H6d | zenon_intro zenon_H77 ]. % 4.67/4.84 apply (zenon_L16_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H72 | zenon_intro zenon_H78 ]. % 4.67/4.84 exact (zenon_H140 zenon_H72). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H79 | zenon_intro zenon_H31 ]. % 4.67/4.84 exact (zenon_H76 zenon_H79). % 4.67/4.84 exact (zenon_H2c zenon_H31). % 4.67/4.84 (* end of lemma zenon_L101_ *) % 4.67/4.84 assert (zenon_L102_ : (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e0)) -> ((op (e3) (e3)) = (e0)) -> False). % 4.67/4.84 do 0 intro. intros zenon_H142 zenon_H80 zenon_H6d. % 4.67/4.84 cut (((op (e2) (e3)) = (e0)) = ((op (e2) (e3)) = (op (e3) (e3)))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_H142. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_H80. % 4.67/4.84 cut (((e0) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H6e]. % 4.67/4.84 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H143]. % 4.67/4.84 congruence. % 4.67/4.84 apply zenon_H143. apply refl_equal. % 4.67/4.84 apply zenon_H6e. apply sym_equal. exact zenon_H6d. % 4.67/4.84 (* end of lemma zenon_L102_ *) % 4.67/4.84 assert (zenon_L103_ : (((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). % 4.67/4.84 do 0 intro. intros zenon_H75 zenon_H80 zenon_H142 zenon_H140 zenon_H76 zenon_H2c. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H75); [ zenon_intro zenon_H6d | zenon_intro zenon_H77 ]. % 4.67/4.84 apply (zenon_L102_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H72 | zenon_intro zenon_H78 ]. % 4.67/4.84 exact (zenon_H140 zenon_H72). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H79 | zenon_intro zenon_H31 ]. % 4.67/4.84 exact (zenon_H76 zenon_H79). % 4.67/4.84 exact (zenon_H2c zenon_H31). % 4.67/4.84 (* end of lemma zenon_L103_ *) % 4.67/4.84 assert (zenon_L104_ : (~((op (e3) (op (e3) (e3))) = (op (e3) (e0)))) -> ((op (e3) (e3)) = (e0)) -> False). % 4.67/4.84 do 0 intro. intros zenon_H144 zenon_H6d. % 4.67/4.84 cut (((op (e3) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H145]. % 4.67/4.84 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H56]. % 4.67/4.84 congruence. % 4.67/4.84 apply zenon_H56. apply refl_equal. % 4.67/4.84 exact (zenon_H145 zenon_H6d). % 4.67/4.84 (* end of lemma zenon_L104_ *) % 4.67/4.84 assert (zenon_L105_ : (~((op (op (e3) (op (e3) (e3))) (op (e3) (e3))) = (op (e1) (e0)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e3) (e0)) = (e1)) -> False). % 4.67/4.84 do 0 intro. intros zenon_H146 zenon_H6d zenon_H123. % 4.67/4.84 cut (((op (e3) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H145]. % 4.67/4.84 cut (((op (e3) (op (e3) (e3))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H147]. % 4.67/4.84 congruence. % 4.67/4.84 cut (((op (e3) (e0)) = (e1)) = ((op (e3) (op (e3) (e3))) = (e1))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_H147. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_H123. % 4.67/4.84 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 4.67/4.84 cut (((op (e3) (e0)) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H148]. % 4.67/4.84 congruence. % 4.67/4.84 elim (classic ((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 4.67/4.84 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3)))) = ((op (e3) (e0)) = (op (e3) (op (e3) (e3))))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_H148. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_H149. % 4.67/4.84 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H14a]. % 4.67/4.84 cut (((op (e3) (op (e3) (e3))) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H144]. % 4.67/4.84 congruence. % 4.67/4.84 apply (zenon_L104_); trivial. % 4.67/4.84 apply zenon_H14a. apply refl_equal. % 4.67/4.84 apply zenon_H14a. apply refl_equal. % 4.67/4.84 apply zenon_H9b. apply refl_equal. % 4.67/4.84 exact (zenon_H145 zenon_H6d). % 4.67/4.84 (* end of lemma zenon_L105_ *) % 4.67/4.84 assert (zenon_L106_ : ((op (e1) (e0)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> ((op (e3) (e3)) = (e0)) -> False). % 4.67/4.84 do 0 intro. intros zenon_Ha1 zenon_H123 zenon_H6d. % 4.67/4.84 apply (zenon_notand_s _ _ ax12); [ zenon_intro zenon_H14c | zenon_intro zenon_H14b ]. % 4.67/4.84 elim (classic ((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 4.67/4.84 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3)))) = ((e1) = (op (e3) (op (e3) (e3))))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_H14c. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_H149. % 4.67/4.84 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H14a]. % 4.67/4.84 cut (((op (e3) (op (e3) (e3))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H147]. % 4.67/4.84 congruence. % 4.67/4.84 cut (((op (e3) (e0)) = (e1)) = ((op (e3) (op (e3) (e3))) = (e1))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_H147. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_H123. % 4.67/4.84 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 4.67/4.84 cut (((op (e3) (e0)) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H148]. % 4.67/4.84 congruence. % 4.67/4.84 elim (classic ((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 4.67/4.84 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3)))) = ((op (e3) (e0)) = (op (e3) (op (e3) (e3))))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_H148. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_H149. % 4.67/4.84 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H14a]. % 4.67/4.84 cut (((op (e3) (op (e3) (e3))) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H144]. % 4.67/4.84 congruence. % 4.67/4.84 apply (zenon_L104_); trivial. % 4.67/4.84 apply zenon_H14a. apply refl_equal. % 4.67/4.84 apply zenon_H14a. apply refl_equal. % 4.67/4.84 apply zenon_H9b. apply refl_equal. % 4.67/4.84 apply zenon_H14a. apply refl_equal. % 4.67/4.84 apply zenon_H14a. apply refl_equal. % 4.67/4.84 apply (zenon_notand_s _ _ zenon_H14b); [ zenon_intro zenon_H6e | zenon_intro zenon_H14d ]. % 4.67/4.84 apply zenon_H6e. apply sym_equal. exact zenon_H6d. % 4.67/4.84 elim (classic ((op (op (e3) (op (e3) (e3))) (op (e3) (e3))) = (op (op (e3) (op (e3) (e3))) (op (e3) (e3))))); [ zenon_intro zenon_H14e | zenon_intro zenon_H14f ]. % 4.67/4.84 cut (((op (op (e3) (op (e3) (e3))) (op (e3) (e3))) = (op (op (e3) (op (e3) (e3))) (op (e3) (e3)))) = ((e2) = (op (op (e3) (op (e3) (e3))) (op (e3) (e3))))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_H14d. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_H14e. % 4.67/4.84 cut (((op (op (e3) (op (e3) (e3))) (op (e3) (e3))) = (op (op (e3) (op (e3) (e3))) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H14f]. % 4.67/4.84 cut (((op (op (e3) (op (e3) (e3))) (op (e3) (e3))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H150]. % 4.67/4.84 congruence. % 4.67/4.84 cut (((op (e1) (e0)) = (e2)) = ((op (op (e3) (op (e3) (e3))) (op (e3) (e3))) = (e2))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_H150. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_Ha1. % 4.67/4.84 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 4.67/4.84 cut (((op (e1) (e0)) = (op (op (e3) (op (e3) (e3))) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H151]. % 4.67/4.84 congruence. % 4.67/4.84 elim (classic ((op (op (e3) (op (e3) (e3))) (op (e3) (e3))) = (op (op (e3) (op (e3) (e3))) (op (e3) (e3))))); [ zenon_intro zenon_H14e | zenon_intro zenon_H14f ]. % 4.67/4.84 cut (((op (op (e3) (op (e3) (e3))) (op (e3) (e3))) = (op (op (e3) (op (e3) (e3))) (op (e3) (e3)))) = ((op (e1) (e0)) = (op (op (e3) (op (e3) (e3))) (op (e3) (e3))))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_H151. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_H14e. % 4.67/4.84 cut (((op (op (e3) (op (e3) (e3))) (op (e3) (e3))) = (op (op (e3) (op (e3) (e3))) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H14f]. % 4.67/4.84 cut (((op (op (e3) (op (e3) (e3))) (op (e3) (e3))) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H146]. % 4.67/4.84 congruence. % 4.67/4.84 apply (zenon_L105_); trivial. % 4.67/4.84 apply zenon_H14f. apply refl_equal. % 4.67/4.84 apply zenon_H14f. apply refl_equal. % 4.67/4.84 apply zenon_H5c. apply refl_equal. % 4.67/4.84 apply zenon_H14f. apply refl_equal. % 4.67/4.84 apply zenon_H14f. apply refl_equal. % 4.67/4.84 (* end of lemma zenon_L106_ *) % 4.67/4.84 assert (zenon_L107_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 4.67/4.84 do 0 intro. intros zenon_H75 zenon_Hbd zenon_H113 zenon_H140 zenon_H76 zenon_H2c. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H75); [ zenon_intro zenon_H6d | zenon_intro zenon_H77 ]. % 4.67/4.84 apply (zenon_L68_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H72 | zenon_intro zenon_H78 ]. % 4.67/4.84 exact (zenon_H140 zenon_H72). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H79 | zenon_intro zenon_H31 ]. % 4.67/4.84 exact (zenon_H76 zenon_H79). % 4.67/4.84 exact (zenon_H2c zenon_H31). % 4.67/4.84 (* end of lemma zenon_L107_ *) % 4.67/4.84 assert (zenon_L108_ : ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (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 (e0) (e3)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((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)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> False). % 4.67/4.84 do 0 intro. intros zenon_H152 zenon_H1d zenon_H137 zenon_Hb3 zenon_H82 zenon_Hdf zenon_H140 zenon_H13e zenon_H117 zenon_H142 zenon_H70 zenon_H75 zenon_H21 zenon_H113 zenon_H114 zenon_H5b zenon_Hb9 zenon_H7b zenon_H135 zenon_H132 zenon_H36 zenon_H7c zenon_H100 zenon_H12e zenon_H76 zenon_H9d zenon_H54 zenon_Hfd zenon_H13c zenon_H103 zenon_H95 zenon_Hd0 zenon_H4c zenon_H94 zenon_Hb4 zenon_H118 zenon_H1e zenon_H11f zenon_H153. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H85 | zenon_intro zenon_H104 ]. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H2c | zenon_intro zenon_H104 ]. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ]. % 4.67/4.84 exact (zenon_H1e zenon_H23). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ]. % 4.67/4.84 apply (zenon_L96_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H24); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H114); [ zenon_intro zenon_H23 | zenon_intro zenon_H115 ]. % 4.67/4.84 exact (zenon_H1e zenon_H23). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H34 | zenon_intro zenon_H116 ]. % 4.67/4.84 apply (zenon_L99_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H42 | zenon_intro zenon_Hbd ]. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_H5a | zenon_intro zenon_H138 ]. % 4.67/4.84 exact (zenon_H5b zenon_H5a). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_H7e | zenon_intro zenon_H139 ]. % 4.67/4.84 exact (zenon_H7c zenon_H7e). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H123 ]. % 4.67/4.84 apply (zenon_L100_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hb5 ]. % 4.67/4.84 exact (zenon_Hb4 zenon_Hb6). % 4.67/4.84 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hb7 ]. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H26 | zenon_intro zenon_H11a ]. % 4.67/4.84 exact (zenon_H21 zenon_H26). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H11a); [ zenon_intro zenon_H7a | zenon_intro zenon_H11b ]. % 4.67/4.84 apply (zenon_L101_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H80 | zenon_intro zenon_H6d ]. % 4.67/4.84 apply (zenon_L103_); trivial. % 4.67/4.84 apply (zenon_L106_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H98 | zenon_intro zenon_Hb0 ]. % 4.67/4.84 exact (zenon_H95 zenon_H98). % 4.67/4.84 apply (zenon_L77_); trivial. % 4.67/4.84 apply (zenon_L107_); trivial. % 4.67/4.84 exact (zenon_H21 zenon_H26). % 4.67/4.84 apply (zenon_L73_); trivial. % 4.67/4.84 apply (zenon_L73_); trivial. % 4.67/4.84 (* end of lemma zenon_L108_ *) % 4.67/4.84 assert (zenon_L109_ : ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (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)))) -> (((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 (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (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) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> False). % 4.67/4.84 do 0 intro. intros zenon_H154 zenon_H153 zenon_H103 zenon_H13c zenon_Hfd zenon_H54 zenon_H113 zenon_H75 zenon_H70 zenon_H142 zenon_H117 zenon_H13e zenon_Hdf zenon_H1d zenon_H21 zenon_H118 zenon_H11f zenon_H76 zenon_H12e zenon_Hb9 zenon_H7c zenon_Hb3 zenon_Haf zenon_H9d zenon_H37 zenon_Ha9 zenon_Ha4 zenon_H4c zenon_Ha0 zenon_H82 zenon_Hac zenon_Hb4 zenon_H95 zenon_H137 zenon_H5b zenon_H94 zenon_Hd0 zenon_H100 zenon_H36 zenon_H132 zenon_H135 zenon_H7b zenon_H114 zenon_H1f zenon_H1e zenon_H152. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H96 | zenon_intro zenon_H140 ]. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H85 | zenon_intro zenon_H104 ]. % 4.67/4.84 apply (zenon_L91_); trivial. % 4.67/4.84 apply (zenon_L73_); trivial. % 4.67/4.84 apply (zenon_L108_); trivial. % 4.67/4.84 (* end of lemma zenon_L109_ *) % 4.67/4.84 assert (zenon_L110_ : ((op (e1) (e0)) = (e0)) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e1))) -> False). % 4.67/4.84 do 0 intro. intros zenon_H34 zenon_H7e zenon_Hb9. % 4.67/4.84 elim (classic ((e1) = (e1))); [ zenon_intro zenon_Hba | zenon_intro zenon_H9b ]. % 4.67/4.84 cut (((e1) = (e1)) = ((e0) = (e1))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_Hb9. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_Hba. % 4.67/4.84 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 4.67/4.84 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hbb]. % 4.67/4.84 congruence. % 4.67/4.84 cut (((op (e1) (e0)) = (e0)) = ((e1) = (e0))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_Hbb. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_H34. % 4.67/4.84 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 4.67/4.84 cut (((op (e1) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H7c]. % 4.67/4.84 congruence. % 4.67/4.84 exact (zenon_H7c zenon_H7e). % 4.67/4.84 apply zenon_H52. apply refl_equal. % 4.67/4.84 apply zenon_H9b. apply refl_equal. % 4.67/4.84 apply zenon_H9b. apply refl_equal. % 4.67/4.84 (* end of lemma zenon_L110_ *) % 4.67/4.84 assert (zenon_L111_ : (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e1)) -> ((op (e3) (e3)) = (e1)) -> False). % 4.67/4.84 do 0 intro. intros zenon_H142 zenon_Hd5 zenon_H72. % 4.67/4.84 cut (((op (e2) (e3)) = (e1)) = ((op (e2) (e3)) = (op (e3) (e3)))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_H142. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_Hd5. % 4.67/4.84 cut (((e1) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 4.67/4.84 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H143]. % 4.67/4.84 congruence. % 4.67/4.84 apply zenon_H143. apply refl_equal. % 4.67/4.84 apply zenon_H73. apply sym_equal. exact zenon_H72. % 4.67/4.84 (* end of lemma zenon_L111_ *) % 4.67/4.84 assert (zenon_L112_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 4.67/4.84 do 0 intro. intros zenon_H75 zenon_H145 zenon_Hd5 zenon_H142 zenon_H76 zenon_H2c. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H75); [ zenon_intro zenon_H6d | zenon_intro zenon_H77 ]. % 4.67/4.84 exact (zenon_H145 zenon_H6d). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H72 | zenon_intro zenon_H78 ]. % 4.67/4.84 apply (zenon_L111_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H79 | zenon_intro zenon_H31 ]. % 4.67/4.84 exact (zenon_H76 zenon_H79). % 4.67/4.84 exact (zenon_H2c zenon_H31). % 4.67/4.84 (* end of lemma zenon_L112_ *) % 4.67/4.84 assert (zenon_L113_ : (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e1)) -> ((op (e3) (e3)) = (e1)) -> False). % 4.67/4.84 do 0 intro. intros zenon_H113 zenon_H123 zenon_H72. % 4.67/4.84 cut (((op (e3) (e0)) = (e1)) = ((op (e3) (e0)) = (op (e3) (e3)))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_H113. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_H123. % 4.67/4.84 cut (((e1) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 4.67/4.84 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 4.67/4.84 congruence. % 4.67/4.84 apply zenon_Hb2. apply refl_equal. % 4.67/4.84 apply zenon_H73. apply sym_equal. exact zenon_H72. % 4.67/4.84 (* end of lemma zenon_L113_ *) % 4.67/4.84 assert (zenon_L114_ : ((op (e0) (e1)) = (e1)) -> ((op (e0) (e1)) = (e3)) -> (~((e1) = (e3))) -> False). % 4.67/4.84 do 0 intro. intros zenon_H9c zenon_Hd1 zenon_H13c. % 4.67/4.84 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H55 | zenon_intro zenon_H56 ]. % 4.67/4.84 cut (((e3) = (e3)) = ((e1) = (e3))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_H13c. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_H55. % 4.67/4.84 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H56]. % 4.67/4.84 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H13d]. % 4.67/4.84 congruence. % 4.67/4.84 cut (((op (e0) (e1)) = (e1)) = ((e3) = (e1))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_H13d. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_H9c. % 4.67/4.84 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 4.67/4.84 cut (((op (e0) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H13b]. % 4.67/4.84 congruence. % 4.67/4.84 exact (zenon_H13b zenon_Hd1). % 4.67/4.84 apply zenon_H9b. apply refl_equal. % 4.67/4.84 apply zenon_H56. apply refl_equal. % 4.67/4.84 apply zenon_H56. apply refl_equal. % 4.67/4.84 (* end of lemma zenon_L114_ *) % 4.67/4.84 assert (zenon_L115_ : ((op (e0) (e3)) = (e2)) -> ((op (e0) (e3)) = (e3)) -> (~((e2) = (e3))) -> False). % 4.67/4.84 do 0 intro. intros zenon_H8a zenon_H8c zenon_Hfd. % 4.67/4.84 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H55 | zenon_intro zenon_H56 ]. % 4.67/4.84 cut (((e3) = (e3)) = ((e2) = (e3))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_Hfd. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_H55. % 4.67/4.84 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H56]. % 4.67/4.84 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hfe]. % 4.67/4.84 congruence. % 4.67/4.84 cut (((op (e0) (e3)) = (e2)) = ((e3) = (e2))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_Hfe. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_H8a. % 4.67/4.84 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 4.67/4.84 cut (((op (e0) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hfb]. % 4.67/4.84 congruence. % 4.67/4.84 exact (zenon_Hfb zenon_H8c). % 4.67/4.84 apply zenon_H5c. apply refl_equal. % 4.67/4.84 apply zenon_H56. apply refl_equal. % 4.67/4.84 apply zenon_H56. apply refl_equal. % 4.67/4.84 (* end of lemma zenon_L115_ *) % 4.67/4.84 assert (zenon_L116_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e2) = (e3))) -> False). % 4.67/4.84 do 0 intro. intros zenon_H100 zenon_Hb4 zenon_H82 zenon_H103 zenon_H123 zenon_H113 zenon_H75 zenon_H145 zenon_H142 zenon_H76 zenon_H2c zenon_H135 zenon_H12e zenon_H9d zenon_H85 zenon_Hdf zenon_H13c zenon_H9c zenon_H54 zenon_H27 zenon_Hfd. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hb6 | zenon_intro zenon_H105 ]. % 4.67/4.84 exact (zenon_Hb4 zenon_Hb6). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H5e | zenon_intro zenon_H106 ]. % 4.67/4.84 apply (zenon_L26_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_H92 | zenon_intro zenon_H8a ]. % 4.67/4.84 apply (zenon_L23_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_H108 | zenon_intro zenon_H107 ]. % 4.67/4.84 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H87 | zenon_intro zenon_He0 ]. % 4.67/4.84 apply (zenon_L93_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H71 | zenon_intro zenon_He1 ]. % 4.67/4.84 exact (zenon_H135 zenon_H71). % 4.67/4.84 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H72 ]. % 4.67/4.84 apply (zenon_L112_); trivial. % 4.67/4.84 apply (zenon_L113_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H109 ]. % 4.67/4.84 apply (zenon_L114_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Hed | zenon_intro zenon_H8c ]. % 4.67/4.84 apply (zenon_L53_); trivial. % 4.67/4.84 apply (zenon_L115_); trivial. % 4.67/4.84 (* end of lemma zenon_L116_ *) % 4.67/4.84 assert (zenon_L117_ : (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e2)) = (e0)) -> False). % 4.67/4.84 do 0 intro. intros zenon_H132 zenon_H27 zenon_He5. % 4.67/4.84 cut (((op (e0) (e2)) = (e0)) = ((op (e0) (e2)) = (op (e1) (e2)))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_H132. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_H27. % 4.67/4.84 cut (((e0) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H155]. % 4.67/4.84 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H134]. % 4.67/4.84 congruence. % 4.67/4.84 apply zenon_H134. apply refl_equal. % 4.67/4.84 apply zenon_H155. apply sym_equal. exact zenon_He5. % 4.67/4.84 (* end of lemma zenon_L117_ *) % 4.67/4.84 assert (zenon_L118_ : ((op (e1) (e0)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> (~((e1) = (e2))) -> False). % 4.67/4.84 do 0 intro. intros zenon_H7e zenon_Ha1 zenon_H9d. % 4.67/4.84 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H83 | zenon_intro zenon_H5c ]. % 4.67/4.84 cut (((e2) = (e2)) = ((e1) = (e2))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_H9d. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_H83. % 4.67/4.84 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 4.67/4.84 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9e]. % 4.67/4.84 congruence. % 4.67/4.84 cut (((op (e1) (e0)) = (e1)) = ((e2) = (e1))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_H9e. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_H7e. % 4.67/4.84 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 4.67/4.84 cut (((op (e1) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hec]. % 4.67/4.84 congruence. % 4.67/4.84 exact (zenon_Hec zenon_Ha1). % 4.67/4.84 apply zenon_H9b. apply refl_equal. % 4.67/4.84 apply zenon_H5c. apply refl_equal. % 4.67/4.84 apply zenon_H5c. apply refl_equal. % 4.67/4.84 (* end of lemma zenon_L118_ *) % 4.67/4.84 assert (zenon_L119_ : ((op (e1) (e0)) = (e1)) -> ((op (e1) (e0)) = (e3)) -> (~((e1) = (e3))) -> False). % 4.67/4.84 do 0 intro. intros zenon_H7e zenon_H156 zenon_H13c. % 4.67/4.84 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H55 | zenon_intro zenon_H56 ]. % 4.67/4.84 cut (((e3) = (e3)) = ((e1) = (e3))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_H13c. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_H55. % 4.67/4.84 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H56]. % 4.67/4.84 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H13d]. % 4.67/4.84 congruence. % 4.67/4.84 cut (((op (e1) (e0)) = (e1)) = ((e3) = (e1))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_H13d. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_H7e. % 4.67/4.84 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 4.67/4.84 cut (((op (e1) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H157]. % 4.67/4.84 congruence. % 4.67/4.84 exact (zenon_H157 zenon_H156). % 4.67/4.84 apply zenon_H9b. apply refl_equal. % 4.67/4.84 apply zenon_H56. apply refl_equal. % 4.67/4.84 apply zenon_H56. apply refl_equal. % 4.67/4.84 (* end of lemma zenon_L119_ *) % 4.67/4.84 assert (zenon_L120_ : (~((op (e1) (op (e1) (e1))) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e3)) -> False). % 4.67/4.84 do 0 intro. intros zenon_H158 zenon_H3f. % 4.67/4.84 cut (((op (e1) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 4.67/4.84 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 4.67/4.84 congruence. % 4.67/4.84 apply zenon_H9b. apply refl_equal. % 4.67/4.84 exact (zenon_H38 zenon_H3f). % 4.67/4.84 (* end of lemma zenon_L120_ *) % 4.67/4.84 assert (zenon_L121_ : ((op (e0) (e3)) = (e2)) -> ((op (e1) (e3)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> False). % 4.67/4.84 do 0 intro. intros zenon_H8a zenon_H7a zenon_H3f. % 4.67/4.84 apply (zenon_notand_s _ _ ax11); [ zenon_intro zenon_H15a | zenon_intro zenon_H159 ]. % 4.67/4.84 elim (classic ((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hc7 ]. % 4.67/4.84 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1)))) = ((e0) = (op (e1) (op (e1) (e1))))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_H15a. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_Hc6. % 4.67/4.84 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_Hc7]. % 4.67/4.84 cut (((op (e1) (op (e1) (e1))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H15b]. % 4.67/4.84 congruence. % 4.67/4.84 cut (((op (e1) (e3)) = (e0)) = ((op (e1) (op (e1) (e1))) = (e0))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_H15b. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_H7a. % 4.67/4.84 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 4.67/4.84 cut (((op (e1) (e3)) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H15c]. % 4.67/4.84 congruence. % 4.67/4.84 elim (classic ((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hc7 ]. % 4.67/4.84 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1)))) = ((op (e1) (e3)) = (op (e1) (op (e1) (e1))))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_H15c. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_Hc6. % 4.67/4.84 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_Hc7]. % 4.67/4.84 cut (((op (e1) (op (e1) (e1))) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H158]. % 4.67/4.84 congruence. % 4.67/4.84 apply (zenon_L120_); trivial. % 4.67/4.84 apply zenon_Hc7. apply refl_equal. % 4.67/4.84 apply zenon_Hc7. apply refl_equal. % 4.67/4.84 apply zenon_H52. apply refl_equal. % 4.67/4.84 apply zenon_Hc7. apply refl_equal. % 4.67/4.84 apply zenon_Hc7. apply refl_equal. % 4.67/4.84 apply (zenon_notand_s _ _ zenon_H159); [ zenon_intro zenon_H15e | zenon_intro zenon_H15d ]. % 4.67/4.84 apply zenon_H15e. apply sym_equal. exact zenon_H3f. % 4.67/4.84 elim (classic ((op (op (e1) (op (e1) (e1))) (op (e1) (e1))) = (op (op (e1) (op (e1) (e1))) (op (e1) (e1))))); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hcc ]. % 4.67/4.84 cut (((op (op (e1) (op (e1) (e1))) (op (e1) (e1))) = (op (op (e1) (op (e1) (e1))) (op (e1) (e1)))) = ((e2) = (op (op (e1) (op (e1) (e1))) (op (e1) (e1))))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_H15d. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_Hcb. % 4.67/4.84 cut (((op (op (e1) (op (e1) (e1))) (op (e1) (e1))) = (op (op (e1) (op (e1) (e1))) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_Hcc]. % 4.67/4.84 cut (((op (op (e1) (op (e1) (e1))) (op (e1) (e1))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H15f]. % 4.67/4.84 congruence. % 4.67/4.84 cut (((op (e0) (e3)) = (e2)) = ((op (op (e1) (op (e1) (e1))) (op (e1) (e1))) = (e2))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_H15f. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_H8a. % 4.67/4.84 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 4.67/4.84 cut (((op (e0) (e3)) = (op (op (e1) (op (e1) (e1))) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H160]. % 4.67/4.84 congruence. % 4.67/4.84 elim (classic ((op (op (e1) (op (e1) (e1))) (op (e1) (e1))) = (op (op (e1) (op (e1) (e1))) (op (e1) (e1))))); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hcc ]. % 4.67/4.84 cut (((op (op (e1) (op (e1) (e1))) (op (e1) (e1))) = (op (op (e1) (op (e1) (e1))) (op (e1) (e1)))) = ((op (e0) (e3)) = (op (op (e1) (op (e1) (e1))) (op (e1) (e1))))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_H160. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_Hcb. % 4.67/4.84 cut (((op (op (e1) (op (e1) (e1))) (op (e1) (e1))) = (op (op (e1) (op (e1) (e1))) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_Hcc]. % 4.67/4.84 cut (((op (op (e1) (op (e1) (e1))) (op (e1) (e1))) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H161]. % 4.67/4.84 congruence. % 4.67/4.84 cut (((op (e1) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 4.67/4.84 cut (((op (e1) (op (e1) (e1))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H15b]. % 4.67/4.84 congruence. % 4.67/4.84 cut (((op (e1) (e3)) = (e0)) = ((op (e1) (op (e1) (e1))) = (e0))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_H15b. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_H7a. % 4.67/4.84 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 4.67/4.84 cut (((op (e1) (e3)) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H15c]. % 4.67/4.84 congruence. % 4.67/4.84 elim (classic ((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hc7 ]. % 4.67/4.84 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1)))) = ((op (e1) (e3)) = (op (e1) (op (e1) (e1))))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_H15c. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_Hc6. % 4.67/4.84 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_Hc7]. % 4.67/4.84 cut (((op (e1) (op (e1) (e1))) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H158]. % 4.67/4.84 congruence. % 4.67/4.84 apply (zenon_L120_); trivial. % 4.67/4.84 apply zenon_Hc7. apply refl_equal. % 4.67/4.84 apply zenon_Hc7. apply refl_equal. % 4.67/4.84 apply zenon_H52. apply refl_equal. % 4.67/4.84 exact (zenon_H38 zenon_H3f). % 4.67/4.84 apply zenon_Hcc. apply refl_equal. % 4.67/4.84 apply zenon_Hcc. apply refl_equal. % 4.67/4.84 apply zenon_H5c. apply refl_equal. % 4.67/4.84 apply zenon_Hcc. apply refl_equal. % 4.67/4.84 apply zenon_Hcc. apply refl_equal. % 4.67/4.84 (* end of lemma zenon_L121_ *) % 4.67/4.84 assert (zenon_L122_ : ((op (e1) (e2)) = (e2)) -> ((op (e1) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 4.67/4.84 do 0 intro. intros zenon_Ha2 zenon_H162 zenon_Hfd. % 4.67/4.84 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H55 | zenon_intro zenon_H56 ]. % 4.67/4.84 cut (((e3) = (e3)) = ((e2) = (e3))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_Hfd. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_H55. % 4.67/4.84 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H56]. % 4.67/4.84 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hfe]. % 4.67/4.84 congruence. % 4.67/4.84 cut (((op (e1) (e2)) = (e2)) = ((e3) = (e2))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_Hfe. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_Ha2. % 4.67/4.84 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 4.67/4.84 cut (((op (e1) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H163]. % 4.67/4.84 congruence. % 4.67/4.84 exact (zenon_H163 zenon_H162). % 4.67/4.84 apply zenon_H5c. apply refl_equal. % 4.67/4.84 apply zenon_H56. apply refl_equal. % 4.67/4.84 apply zenon_H56. apply refl_equal. % 4.67/4.84 (* end of lemma zenon_L122_ *) % 4.67/4.84 assert (zenon_L123_ : ((op (e1) (e3)) = (e0)) -> ((op (e1) (e3)) = (e3)) -> (~((e0) = (e3))) -> False). % 4.67/4.84 do 0 intro. intros zenon_H7a zenon_Hdb zenon_H54. % 4.67/4.84 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H55 | zenon_intro zenon_H56 ]. % 4.67/4.84 cut (((e3) = (e3)) = ((e0) = (e3))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_H54. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_H55. % 4.67/4.84 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H56]. % 4.67/4.84 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 4.67/4.84 congruence. % 4.67/4.84 cut (((op (e1) (e3)) = (e0)) = ((e3) = (e0))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_H57. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_H7a. % 4.67/4.84 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 4.67/4.84 cut (((op (e1) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H164]. % 4.67/4.84 congruence. % 4.67/4.84 exact (zenon_H164 zenon_Hdb). % 4.67/4.84 apply zenon_H52. apply refl_equal. % 4.67/4.84 apply zenon_H56. apply refl_equal. % 4.67/4.84 apply zenon_H56. apply refl_equal. % 4.67/4.84 (* end of lemma zenon_L123_ *) % 4.67/4.84 assert (zenon_L124_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e1) (e3)) = (e2)) -> False). % 4.67/4.84 do 0 intro. intros zenon_H86 zenon_H8a zenon_Hd8. % 4.67/4.84 cut (((op (e0) (e3)) = (e2)) = ((op (e0) (e3)) = (op (e1) (e3)))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_H86. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_H8a. % 4.67/4.84 cut (((e2) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd9]. % 4.67/4.84 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 4.67/4.84 congruence. % 4.67/4.84 apply zenon_H6f. apply refl_equal. % 4.67/4.84 apply zenon_Hd9. apply sym_equal. exact zenon_Hd8. % 4.67/4.84 (* end of lemma zenon_L124_ *) % 4.67/4.84 assert (zenon_L125_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e0))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((e0) = (e3))) -> (~((e2) = (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) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> False). % 4.67/4.84 do 0 intro. intros zenon_He9 zenon_Hbe zenon_Hbd zenon_Hc3 zenon_H27 zenon_H132 zenon_H165 zenon_H9d zenon_H37 zenon_H54 zenon_Hfd zenon_H7e zenon_H13c zenon_H166 zenon_H86 zenon_H8a. % 4.67/4.84 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H34 | zenon_intro zenon_Hea ]. % 4.67/4.84 apply (zenon_L36_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H3a | zenon_intro zenon_Heb ]. % 4.67/4.84 exact (zenon_Hc3 zenon_H3a). % 4.67/4.84 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_He5 | zenon_intro zenon_H7a ]. % 4.67/4.84 apply (zenon_L117_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_Ha1 | zenon_intro zenon_H167 ]. % 4.67/4.84 apply (zenon_L118_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H167); [ zenon_intro zenon_H40 | zenon_intro zenon_H168 ]. % 4.67/4.84 exact (zenon_H37 zenon_H40). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hd8 ]. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H156 | zenon_intro zenon_H169 ]. % 4.67/4.84 apply (zenon_L119_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H3f | zenon_intro zenon_H16a ]. % 4.67/4.84 apply (zenon_L121_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H162 | zenon_intro zenon_Hdb ]. % 4.67/4.84 apply (zenon_L122_); trivial. % 4.67/4.84 apply (zenon_L123_); trivial. % 4.67/4.84 apply (zenon_L124_); trivial. % 4.67/4.84 (* end of lemma zenon_L125_ *) % 4.67/4.84 assert (zenon_L126_ : (((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) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e0))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((e0) = (e3))) -> (~((e2) = (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) (e3)) = (op (e1) (e3)))) -> False). % 4.67/4.84 do 0 intro. intros zenon_H100 zenon_Hb4 zenon_H9c zenon_H82 zenon_He9 zenon_Hbe zenon_Hbd zenon_Hc3 zenon_H27 zenon_H132 zenon_H165 zenon_H9d zenon_H37 zenon_H54 zenon_Hfd zenon_H7e zenon_H13c zenon_H166 zenon_H86. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hb6 | zenon_intro zenon_H105 ]. % 4.67/4.84 exact (zenon_Hb4 zenon_Hb6). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H5e | zenon_intro zenon_H106 ]. % 4.67/4.84 apply (zenon_L26_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_H92 | zenon_intro zenon_H8a ]. % 4.67/4.84 apply (zenon_L23_); trivial. % 4.67/4.84 apply (zenon_L125_); trivial. % 4.67/4.84 (* end of lemma zenon_L126_ *) % 4.67/4.84 assert (zenon_L127_ : (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (e1)) = (e1)) -> False). % 4.67/4.84 do 0 intro. intros zenon_Hd0 zenon_H9c zenon_Hf1. % 4.67/4.84 cut (((op (e0) (e1)) = (e1)) = ((op (e0) (e1)) = (op (e2) (e1)))). % 4.67/4.84 intro zenon_D_pnotp. % 4.67/4.84 apply zenon_Hd0. % 4.67/4.84 rewrite <- zenon_D_pnotp. % 4.67/4.84 exact zenon_H9c. % 4.67/4.84 cut (((e1) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hf2]. % 4.67/4.84 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hd3]. % 4.67/4.84 congruence. % 4.67/4.84 apply zenon_Hd3. apply refl_equal. % 4.67/4.84 apply zenon_Hf2. apply sym_equal. exact zenon_Hf1. % 4.67/4.84 (* end of lemma zenon_L127_ *) % 4.67/4.84 assert (zenon_L128_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 4.67/4.84 do 0 intro. intros zenon_H16b zenon_H9d zenon_H98 zenon_H9c zenon_Hd0 zenon_H16c zenon_H75 zenon_H145 zenon_H142 zenon_H76 zenon_H2c. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H16d ]. % 4.67/4.84 apply (zenon_L75_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H16e ]. % 4.67/4.84 apply (zenon_L127_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_H48 | zenon_intro zenon_Hd5 ]. % 4.67/4.84 exact (zenon_H16c zenon_H48). % 4.67/4.84 apply (zenon_L112_); trivial. % 4.67/4.84 (* end of lemma zenon_L128_ *) % 4.67/4.84 assert (zenon_L129_ : ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (~((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 (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 4.67/4.84 do 0 intro. intros zenon_H153 zenon_H1e zenon_H1f zenon_H114 zenon_Ha9 zenon_Ha4 zenon_H4c zenon_Ha0 zenon_H5b zenon_Hb3 zenon_H37 zenon_H96 zenon_Haf zenon_Hac zenon_H9d zenon_Hd0 zenon_H16c zenon_H75 zenon_H76 zenon_H142 zenon_H145 zenon_H16b zenon_H82 zenon_Hb4 zenon_Hb9 zenon_H12e zenon_H85 zenon_H11f zenon_H118 zenon_H21 zenon_H1d. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H2c | zenon_intro zenon_H104 ]. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ]. % 4.67/4.84 exact (zenon_H1e zenon_H23). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ]. % 4.67/4.84 exact (zenon_H1f zenon_H25). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H24); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H114); [ zenon_intro zenon_H23 | zenon_intro zenon_H115 ]. % 4.67/4.84 exact (zenon_H1e zenon_H23). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H34 | zenon_intro zenon_H116 ]. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H5a | zenon_intro zenon_H119 ]. % 4.67/4.84 exact (zenon_H5b zenon_H5a). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H9c | zenon_intro zenon_H11c ]. % 4.67/4.84 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hb5 ]. % 4.67/4.84 exact (zenon_Hb4 zenon_Hb6). % 4.67/4.84 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hb7 ]. % 4.67/4.84 apply (zenon_L52_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H98 | zenon_intro zenon_Hb0 ]. % 4.67/4.84 apply (zenon_L128_); trivial. % 4.67/4.84 apply (zenon_L33_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H87 ]. % 4.67/4.84 apply (zenon_L35_); trivial. % 4.67/4.84 apply (zenon_L83_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H42 | zenon_intro zenon_Hbd ]. % 4.67/4.84 apply (zenon_L84_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H5a | zenon_intro zenon_H119 ]. % 4.67/4.84 exact (zenon_H5b zenon_H5a). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H9c | zenon_intro zenon_H11c ]. % 4.67/4.84 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hb5 ]. % 4.67/4.84 exact (zenon_Hb4 zenon_Hb6). % 4.67/4.84 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hb7 ]. % 4.67/4.84 apply (zenon_L30_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H98 | zenon_intro zenon_Hb0 ]. % 4.67/4.84 apply (zenon_L128_); trivial. % 4.67/4.84 apply (zenon_L61_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H87 ]. % 4.67/4.84 apply (zenon_L35_); trivial. % 4.67/4.84 apply (zenon_L83_); trivial. % 4.67/4.84 exact (zenon_H21 zenon_H26). % 4.67/4.84 apply (zenon_L73_); trivial. % 4.67/4.84 (* end of lemma zenon_L129_ *) % 4.67/4.84 assert (zenon_L130_ : ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> False). % 4.67/4.84 do 0 intro. intros zenon_H153 zenon_H1e zenon_H5b zenon_Hb4 zenon_H11f zenon_H145 zenon_H140 zenon_H76 zenon_H75. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H2c | zenon_intro zenon_H104 ]. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H75); [ zenon_intro zenon_H6d | zenon_intro zenon_H77 ]. % 4.67/4.84 exact (zenon_H145 zenon_H6d). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H72 | zenon_intro zenon_H78 ]. % 4.67/4.84 exact (zenon_H140 zenon_H72). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H79 | zenon_intro zenon_H31 ]. % 4.67/4.84 exact (zenon_H76 zenon_H79). % 4.67/4.84 exact (zenon_H2c zenon_H31). % 4.67/4.84 apply (zenon_L73_); trivial. % 4.67/4.84 (* end of lemma zenon_L130_ *) % 4.67/4.84 assert (zenon_L131_ : ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((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 (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> False). % 4.67/4.84 do 0 intro. intros zenon_H154 zenon_H153 zenon_H1e zenon_H1f zenon_H114 zenon_Ha9 zenon_Ha4 zenon_H4c zenon_Ha0 zenon_H5b zenon_Hb3 zenon_H37 zenon_Haf zenon_Hac zenon_H9d zenon_Hd0 zenon_H16c zenon_H75 zenon_H76 zenon_H142 zenon_H145 zenon_H16b zenon_H82 zenon_Hb4 zenon_Hb9 zenon_H12e zenon_H11f zenon_H118 zenon_H21 zenon_H1d zenon_H152. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_H96 | zenon_intro zenon_H140 ]. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H85 | zenon_intro zenon_H104 ]. % 4.67/4.84 apply (zenon_L129_); trivial. % 4.67/4.84 apply (zenon_L73_); trivial. % 4.67/4.84 apply (zenon_L130_); trivial. % 4.67/4.84 (* end of lemma zenon_L131_ *) % 4.67/4.84 assert (zenon_L132_ : ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((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))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e1) (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)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> False). % 4.67/4.84 do 0 intro. intros zenon_H16f zenon_H16b zenon_Hd0 zenon_H154 zenon_H153 zenon_H1e zenon_H1f zenon_H114 zenon_He9 zenon_H166 zenon_H86 zenon_H165 zenon_H132 zenon_Hc3 zenon_Hbe zenon_H5b zenon_H137 zenon_H103 zenon_Hfd zenon_H54 zenon_H13c zenon_H12e zenon_H76 zenon_H135 zenon_H75 zenon_H142 zenon_H145 zenon_H113 zenon_Hdf zenon_H100 zenon_Hb4 zenon_Hac zenon_H82 zenon_Ha0 zenon_H4c zenon_Ha4 zenon_Ha9 zenon_H37 zenon_H9d zenon_Haf zenon_Hb3 zenon_Hb9 zenon_H11f zenon_H118 zenon_H21 zenon_H1d zenon_H152. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H96 | zenon_intro zenon_H16c ]. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H85 | zenon_intro zenon_H104 ]. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H2c | zenon_intro zenon_H104 ]. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ]. % 4.67/4.84 exact (zenon_H1e zenon_H23). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ]. % 4.67/4.84 exact (zenon_H1f zenon_H25). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H24); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H114); [ zenon_intro zenon_H23 | zenon_intro zenon_H115 ]. % 4.67/4.84 exact (zenon_H1e zenon_H23). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H34 | zenon_intro zenon_H116 ]. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H5a | zenon_intro zenon_H119 ]. % 4.67/4.84 exact (zenon_H5b zenon_H5a). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H9c | zenon_intro zenon_H11c ]. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_H5a | zenon_intro zenon_H138 ]. % 4.67/4.84 exact (zenon_H5b zenon_H5a). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_H7e | zenon_intro zenon_H139 ]. % 4.67/4.84 apply (zenon_L110_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H123 ]. % 4.67/4.84 apply (zenon_L76_); trivial. % 4.67/4.84 apply (zenon_L116_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H87 ]. % 4.67/4.84 apply (zenon_L35_); trivial. % 4.67/4.84 apply (zenon_L83_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H42 | zenon_intro zenon_Hbd ]. % 4.67/4.84 apply (zenon_L84_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H5a | zenon_intro zenon_H119 ]. % 4.67/4.84 exact (zenon_H5b zenon_H5a). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H9c | zenon_intro zenon_H11c ]. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_H5a | zenon_intro zenon_H138 ]. % 4.67/4.84 exact (zenon_H5b zenon_H5a). % 4.67/4.84 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_H7e | zenon_intro zenon_H139 ]. % 4.67/4.84 apply (zenon_L126_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H123 ]. % 4.67/4.84 apply (zenon_L76_); trivial. % 4.67/4.84 apply (zenon_L86_); trivial. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H87 ]. % 4.67/4.84 apply (zenon_L35_); trivial. % 4.67/4.84 apply (zenon_L83_); trivial. % 4.67/4.84 exact (zenon_H21 zenon_H26). % 4.67/4.84 apply (zenon_L73_); trivial. % 4.67/4.84 apply (zenon_L73_); trivial. % 4.67/4.84 apply (zenon_L131_); trivial. % 4.67/4.84 (* end of lemma zenon_L132_ *) % 4.67/4.84 assert (zenon_L133_ : ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (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)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (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 (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (e0))) -> (((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 (e2) (e0)) = (op (e2) (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 (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> False). % 4.67/4.84 do 0 intro. intros zenon_H170 zenon_Hbe zenon_Hc3 zenon_H165 zenon_H86 zenon_H166 zenon_He9 zenon_H16b zenon_H16f zenon_H152 zenon_H1e zenon_H1f zenon_H114 zenon_H7b zenon_H135 zenon_H132 zenon_H36 zenon_H100 zenon_Hd0 zenon_H94 zenon_H5b zenon_H137 zenon_Hb4 zenon_Hac zenon_H82 zenon_Ha0 zenon_H4c zenon_Ha4 zenon_Ha9 zenon_H37 zenon_H9d zenon_Haf zenon_Hb3 zenon_H7c zenon_Hb9 zenon_H12e zenon_H76 zenon_H11f zenon_H118 zenon_H21 zenon_H1d zenon_Hdf zenon_H13e zenon_H117 zenon_H142 zenon_H70 zenon_H75 zenon_H113 zenon_H54 zenon_Hfd zenon_H13c zenon_H103 zenon_H153 zenon_H154. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H95 | zenon_intro zenon_H145 ]. % 4.67/4.84 apply (zenon_L109_); trivial. % 4.67/4.84 apply (zenon_L132_); trivial. % 4.67/4.84 (* end of lemma zenon_L133_ *) % 4.67/4.84 assert (zenon_L134_ : ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (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)))) -> (((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 (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((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) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (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)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> False). % 4.67/4.84 do 0 intro. intros zenon_H171 zenon_H154 zenon_H153 zenon_H103 zenon_H13c zenon_Hfd zenon_H54 zenon_H113 zenon_H75 zenon_H70 zenon_H142 zenon_H117 zenon_H13e zenon_Hdf zenon_H1d zenon_H21 zenon_H118 zenon_H11f zenon_H76 zenon_H12e zenon_Hb9 zenon_H7c zenon_Hb3 zenon_Haf zenon_H9d zenon_H37 zenon_Ha9 zenon_Ha4 zenon_H4c zenon_Ha0 zenon_H82 zenon_Hac zenon_Hb4 zenon_H137 zenon_H5b zenon_H94 zenon_Hd0 zenon_H100 zenon_H36 zenon_H132 zenon_H7b zenon_H114 zenon_H1f zenon_H1e zenon_H152 zenon_H170 zenon_Hbe zenon_H165 zenon_H86 zenon_H166 zenon_He9 zenon_H16b zenon_H16f zenon_H172. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H135 | zenon_intro zenon_H104 ]. % 4.67/4.84 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H95 | zenon_intro zenon_Hc3 ]. % 4.67/4.84 apply (zenon_L109_); trivial. % 4.67/4.84 apply (zenon_L133_); trivial. % 4.67/4.84 apply (zenon_L73_); trivial. % 4.67/4.84 (* end of lemma zenon_L134_ *) % 4.67/4.84 assert (zenon_L135_ : ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (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 (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> False). % 4.69/4.85 do 0 intro. intros zenon_H171 zenon_H152 zenon_H1d zenon_H21 zenon_H118 zenon_H11f zenon_Hb9 zenon_Hb3 zenon_Haf zenon_H9d zenon_H37 zenon_Ha9 zenon_Ha4 zenon_H4c zenon_Ha0 zenon_H82 zenon_Hac zenon_Hb4 zenon_H100 zenon_Hdf zenon_H113 zenon_H145 zenon_H142 zenon_H75 zenon_H76 zenon_H12e zenon_H13c zenon_H54 zenon_Hfd zenon_H103 zenon_H137 zenon_H5b zenon_Hbe zenon_Hc3 zenon_H132 zenon_H165 zenon_H86 zenon_H166 zenon_He9 zenon_H114 zenon_H1f zenon_H1e zenon_H153 zenon_H154 zenon_Hd0 zenon_H16b zenon_H16f. % 4.69/4.85 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H135 | zenon_intro zenon_H104 ]. % 4.69/4.85 apply (zenon_L132_); trivial. % 4.69/4.85 apply (zenon_L73_); trivial. % 4.69/4.85 (* end of lemma zenon_L135_ *) % 4.69/4.85 assert (zenon_L136_ : ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (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)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (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 (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (e0))) -> (((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 (e2) (e0)) = (op (e2) (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 (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> False). % 4.69/4.85 do 0 intro. intros zenon_H173 zenon_H170 zenon_Hbe zenon_Hc3 zenon_H165 zenon_H86 zenon_H166 zenon_He9 zenon_H16b zenon_H16f zenon_H152 zenon_H1e zenon_H1f zenon_H114 zenon_H7b zenon_H132 zenon_H36 zenon_H100 zenon_Hd0 zenon_H94 zenon_H5b zenon_H137 zenon_Hb4 zenon_Hac zenon_H82 zenon_Ha0 zenon_H4c zenon_Ha4 zenon_Ha9 zenon_H37 zenon_H9d zenon_Haf zenon_Hb3 zenon_Hb9 zenon_H12e zenon_H76 zenon_H11f zenon_H118 zenon_H21 zenon_H1d zenon_Hdf zenon_H13e zenon_H117 zenon_H142 zenon_H70 zenon_H75 zenon_H113 zenon_H54 zenon_Hfd zenon_H13c zenon_H103 zenon_H153 zenon_H154 zenon_H171. % 4.69/4.85 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H7c | zenon_intro zenon_H145 ]. % 4.69/4.85 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H135 | zenon_intro zenon_H104 ]. % 4.69/4.85 apply (zenon_L133_); trivial. % 4.69/4.85 apply (zenon_L73_); trivial. % 4.69/4.85 apply (zenon_L135_); trivial. % 4.69/4.85 (* end of lemma zenon_L136_ *) % 4.69/4.85 assert (zenon_L137_ : ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (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)))) -> (((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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((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) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (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)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> False). % 4.69/4.85 do 0 intro. intros zenon_H122 zenon_H171 zenon_H154 zenon_H153 zenon_H103 zenon_H13c zenon_Hfd zenon_H54 zenon_H113 zenon_H75 zenon_H70 zenon_H142 zenon_H117 zenon_H13e zenon_Hdf zenon_H1d zenon_H118 zenon_H11f zenon_H76 zenon_H12e zenon_Hb9 zenon_Hb3 zenon_Haf zenon_H9d zenon_H37 zenon_Ha9 zenon_Ha4 zenon_H4c zenon_Ha0 zenon_H82 zenon_Hac zenon_Hb4 zenon_H137 zenon_H5b zenon_H94 zenon_Hd0 zenon_H100 zenon_H36 zenon_H132 zenon_H7b zenon_H114 zenon_H1f zenon_H1e zenon_H152 zenon_H170 zenon_Hbe zenon_H165 zenon_H86 zenon_H166 zenon_He9 zenon_H16b zenon_H16f zenon_H172 zenon_H173 zenon_H174. % 4.69/4.85 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_H21 | zenon_intro zenon_H104 ]. % 4.69/4.85 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H7c | zenon_intro zenon_Hc3 ]. % 4.69/4.85 apply (zenon_L134_); trivial. % 4.69/4.85 apply (zenon_L136_); trivial. % 4.69/4.85 apply (zenon_L73_); trivial. % 4.69/4.85 (* end of lemma zenon_L137_ *) % 4.69/4.85 assert (zenon_L138_ : ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (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))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (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 (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> False). % 4.69/4.85 do 0 intro. intros zenon_H175 zenon_H176 zenon_H174 zenon_H173 zenon_H172 zenon_H16f zenon_H16b zenon_He9 zenon_H166 zenon_H86 zenon_H165 zenon_Hbe zenon_H170 zenon_H152 zenon_H114 zenon_H7b zenon_H132 zenon_H36 zenon_H100 zenon_Hd0 zenon_H94 zenon_H137 zenon_Hac zenon_H82 zenon_Ha0 zenon_Ha4 zenon_Ha9 zenon_H9d zenon_Haf zenon_Hb3 zenon_Hb9 zenon_H12e zenon_H118 zenon_Hdf zenon_H13e zenon_H117 zenon_H142 zenon_H70 zenon_H75 zenon_H113 zenon_H54 zenon_Hfd zenon_H13c zenon_H103 zenon_H153 zenon_H154 zenon_H171 zenon_H177 zenon_H1d zenon_H1f zenon_H1e zenon_H11f zenon_Hb4 zenon_H5b zenon_H122. % 4.69/4.85 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H20 | zenon_intro zenon_H37 ]. % 4.69/4.85 apply (zenon_L74_); trivial. % 4.69/4.85 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_H20 | zenon_intro zenon_H4c ]. % 4.69/4.85 apply (zenon_L74_); trivial. % 4.69/4.85 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H20 | zenon_intro zenon_H76 ]. % 4.69/4.85 apply (zenon_L74_); trivial. % 4.69/4.85 apply (zenon_L137_); trivial. % 4.69/4.85 (* end of lemma zenon_L138_ *) % 4.69/4.85 assert (zenon_L139_ : (~((op (e2) (op (e2) (e2))) = (op (e2) (e0)))) -> ((op (e2) (e2)) = (e0)) -> False). % 4.69/4.85 do 0 intro. intros zenon_H178 zenon_H43. % 4.69/4.85 cut (((op (e2) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H179]. % 4.69/4.85 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 4.69/4.85 congruence. % 4.69/4.85 apply zenon_H5c. apply refl_equal. % 4.69/4.85 exact (zenon_H179 zenon_H43). % 4.69/4.85 (* end of lemma zenon_L139_ *) % 4.69/4.85 assert (zenon_L140_ : (~((op (op (e2) (op (e2) (e2))) (op (e2) (e2))) = (op (e1) (e0)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> False). % 4.69/4.85 do 0 intro. intros zenon_H17a zenon_H43 zenon_Hf0. % 4.69/4.85 cut (((op (e2) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H179]. % 4.69/4.85 cut (((op (e2) (op (e2) (e2))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H17b]. % 4.69/4.85 congruence. % 4.69/4.85 cut (((op (e2) (e0)) = (e1)) = ((op (e2) (op (e2) (e2))) = (e1))). % 4.69/4.85 intro zenon_D_pnotp. % 4.69/4.85 apply zenon_H17b. % 4.69/4.85 rewrite <- zenon_D_pnotp. % 4.69/4.85 exact zenon_Hf0. % 4.69/4.85 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 4.69/4.85 cut (((op (e2) (e0)) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H17c]. % 4.69/4.85 congruence. % 4.69/4.85 elim (classic ((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [ zenon_intro zenon_H17d | zenon_intro zenon_H17e ]. % 4.69/4.85 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2)))) = ((op (e2) (e0)) = (op (e2) (op (e2) (e2))))). % 4.69/4.85 intro zenon_D_pnotp. % 4.69/4.85 apply zenon_H17c. % 4.69/4.85 rewrite <- zenon_D_pnotp. % 4.69/4.85 exact zenon_H17d. % 4.69/4.85 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H17e]. % 4.69/4.85 cut (((op (e2) (op (e2) (e2))) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H178]. % 4.69/4.85 congruence. % 4.69/4.85 apply (zenon_L139_); trivial. % 4.69/4.85 apply zenon_H17e. apply refl_equal. % 4.69/4.85 apply zenon_H17e. apply refl_equal. % 4.69/4.85 apply zenon_H9b. apply refl_equal. % 4.69/4.85 exact (zenon_H179 zenon_H43). % 4.69/4.85 (* end of lemma zenon_L140_ *) % 4.69/4.85 assert (zenon_L141_ : ((op (e1) (e0)) = (e3)) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (e2)) = (e0)) -> False). % 4.69/4.85 do 0 intro. intros zenon_H156 zenon_Hf0 zenon_H43. % 4.69/4.85 apply (zenon_notand_s _ _ ax13); [ zenon_intro zenon_H180 | zenon_intro zenon_H17f ]. % 4.69/4.85 elim (classic ((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [ zenon_intro zenon_H17d | zenon_intro zenon_H17e ]. % 4.69/4.85 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2)))) = ((e1) = (op (e2) (op (e2) (e2))))). % 4.69/4.85 intro zenon_D_pnotp. % 4.69/4.85 apply zenon_H180. % 4.69/4.85 rewrite <- zenon_D_pnotp. % 4.69/4.85 exact zenon_H17d. % 4.69/4.85 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H17e]. % 4.69/4.85 cut (((op (e2) (op (e2) (e2))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H17b]. % 4.69/4.85 congruence. % 4.69/4.85 cut (((op (e2) (e0)) = (e1)) = ((op (e2) (op (e2) (e2))) = (e1))). % 4.69/4.85 intro zenon_D_pnotp. % 4.69/4.85 apply zenon_H17b. % 4.69/4.85 rewrite <- zenon_D_pnotp. % 4.69/4.85 exact zenon_Hf0. % 4.69/4.85 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 4.69/4.85 cut (((op (e2) (e0)) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H17c]. % 4.69/4.85 congruence. % 4.69/4.85 elim (classic ((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [ zenon_intro zenon_H17d | zenon_intro zenon_H17e ]. % 4.69/4.85 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2)))) = ((op (e2) (e0)) = (op (e2) (op (e2) (e2))))). % 4.69/4.85 intro zenon_D_pnotp. % 4.69/4.85 apply zenon_H17c. % 4.69/4.85 rewrite <- zenon_D_pnotp. % 4.69/4.85 exact zenon_H17d. % 4.69/4.85 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H17e]. % 4.69/4.85 cut (((op (e2) (op (e2) (e2))) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H178]. % 4.69/4.85 congruence. % 4.69/4.85 apply (zenon_L139_); trivial. % 4.69/4.85 apply zenon_H17e. apply refl_equal. % 4.69/4.85 apply zenon_H17e. apply refl_equal. % 4.69/4.85 apply zenon_H9b. apply refl_equal. % 4.69/4.85 apply zenon_H17e. apply refl_equal. % 4.69/4.85 apply zenon_H17e. apply refl_equal. % 4.69/4.85 apply (zenon_notand_s _ _ zenon_H17f); [ zenon_intro zenon_H44 | zenon_intro zenon_H181 ]. % 4.69/4.85 apply zenon_H44. apply sym_equal. exact zenon_H43. % 4.69/4.85 elim (classic ((op (op (e2) (op (e2) (e2))) (op (e2) (e2))) = (op (op (e2) (op (e2) (e2))) (op (e2) (e2))))); [ zenon_intro zenon_H182 | zenon_intro zenon_H183 ]. % 4.69/4.85 cut (((op (op (e2) (op (e2) (e2))) (op (e2) (e2))) = (op (op (e2) (op (e2) (e2))) (op (e2) (e2)))) = ((e3) = (op (op (e2) (op (e2) (e2))) (op (e2) (e2))))). % 4.69/4.85 intro zenon_D_pnotp. % 4.69/4.85 apply zenon_H181. % 4.69/4.85 rewrite <- zenon_D_pnotp. % 4.69/4.85 exact zenon_H182. % 4.69/4.85 cut (((op (op (e2) (op (e2) (e2))) (op (e2) (e2))) = (op (op (e2) (op (e2) (e2))) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H183]. % 4.69/4.85 cut (((op (op (e2) (op (e2) (e2))) (op (e2) (e2))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H184]. % 4.69/4.85 congruence. % 4.69/4.85 cut (((op (e1) (e0)) = (e3)) = ((op (op (e2) (op (e2) (e2))) (op (e2) (e2))) = (e3))). % 4.69/4.85 intro zenon_D_pnotp. % 4.69/4.85 apply zenon_H184. % 4.69/4.85 rewrite <- zenon_D_pnotp. % 4.69/4.85 exact zenon_H156. % 4.69/4.85 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H56]. % 4.69/4.85 cut (((op (e1) (e0)) = (op (op (e2) (op (e2) (e2))) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H185]. % 4.69/4.85 congruence. % 4.69/4.85 elim (classic ((op (op (e2) (op (e2) (e2))) (op (e2) (e2))) = (op (op (e2) (op (e2) (e2))) (op (e2) (e2))))); [ zenon_intro zenon_H182 | zenon_intro zenon_H183 ]. % 4.69/4.85 cut (((op (op (e2) (op (e2) (e2))) (op (e2) (e2))) = (op (op (e2) (op (e2) (e2))) (op (e2) (e2)))) = ((op (e1) (e0)) = (op (op (e2) (op (e2) (e2))) (op (e2) (e2))))). % 4.69/4.85 intro zenon_D_pnotp. % 4.69/4.85 apply zenon_H185. % 4.69/4.85 rewrite <- zenon_D_pnotp. % 4.69/4.85 exact zenon_H182. % 4.69/4.85 cut (((op (op (e2) (op (e2) (e2))) (op (e2) (e2))) = (op (op (e2) (op (e2) (e2))) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H183]. % 4.69/4.85 cut (((op (op (e2) (op (e2) (e2))) (op (e2) (e2))) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H17a]. % 4.69/4.85 congruence. % 4.69/4.85 apply (zenon_L140_); trivial. % 4.69/4.85 apply zenon_H183. apply refl_equal. % 4.69/4.85 apply zenon_H183. apply refl_equal. % 4.69/4.85 apply zenon_H56. apply refl_equal. % 4.69/4.85 apply zenon_H183. apply refl_equal. % 4.69/4.85 apply zenon_H183. apply refl_equal. % 4.69/4.85 (* end of lemma zenon_L141_ *) % 4.69/4.85 assert (zenon_L142_ : ((op (e2) (e0)) = (e1)) -> ((op (e2) (e0)) = (e3)) -> (~((e1) = (e3))) -> False). % 4.69/4.85 do 0 intro. intros zenon_Hf0 zenon_H53 zenon_H13c. % 4.69/4.85 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H55 | zenon_intro zenon_H56 ]. % 4.69/4.85 cut (((e3) = (e3)) = ((e1) = (e3))). % 4.69/4.85 intro zenon_D_pnotp. % 4.69/4.85 apply zenon_H13c. % 4.69/4.85 rewrite <- zenon_D_pnotp. % 4.69/4.85 exact zenon_H55. % 4.69/4.85 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H56]. % 4.69/4.85 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H13d]. % 4.69/4.85 congruence. % 4.69/4.85 cut (((op (e2) (e0)) = (e1)) = ((e3) = (e1))). % 4.69/4.85 intro zenon_D_pnotp. % 4.69/4.85 apply zenon_H13d. % 4.69/4.85 rewrite <- zenon_D_pnotp. % 4.69/4.85 exact zenon_Hf0. % 4.69/4.85 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 4.69/4.85 cut (((op (e2) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 4.69/4.85 congruence. % 4.69/4.85 exact (zenon_H58 zenon_H53). % 4.69/4.85 apply zenon_H9b. apply refl_equal. % 4.69/4.85 apply zenon_H56. apply refl_equal. % 4.69/4.85 apply zenon_H56. apply refl_equal. % 4.69/4.85 (* end of lemma zenon_L142_ *) % 4.69/4.85 assert (zenon_L143_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (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))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e3) (e0)) = (e3))) -> False). % 4.69/4.85 do 0 intro. intros zenon_H186 zenon_H104 zenon_H4d zenon_H4c zenon_H16c zenon_H4b zenon_H13c zenon_Hf0 zenon_H29. % 4.69/4.85 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H108 | zenon_intro zenon_H187 ]. % 4.69/4.85 exact (zenon_H104 zenon_H108). % 4.69/4.85 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H156 | zenon_intro zenon_H188 ]. % 4.69/4.85 apply (zenon_or_s _ _ zenon_H4b); [ zenon_intro zenon_H43 | zenon_intro zenon_H4e ]. % 4.69/4.85 apply (zenon_L141_); trivial. % 4.69/4.85 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H48 | zenon_intro zenon_H4f ]. % 4.69/4.85 exact (zenon_H16c zenon_H48). % 4.69/4.85 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H51 | zenon_intro zenon_H50 ]. % 4.69/4.85 exact (zenon_H4c zenon_H51). % 4.69/4.85 exact (zenon_H4d zenon_H50). % 4.69/4.85 apply (zenon_or_s _ _ zenon_H188); [ zenon_intro zenon_H53 | zenon_intro zenon_H2e ]. % 4.69/4.85 apply (zenon_L142_); trivial. % 4.69/4.85 exact (zenon_H29 zenon_H2e). % 4.69/4.85 (* end of lemma zenon_L143_ *) % 4.69/4.85 assert (zenon_L144_ : ((op (e0) (e2)) = (e1)) -> ((op (e0) (e2)) = (e3)) -> (~((e1) = (e3))) -> False). % 4.69/4.85 do 0 intro. intros zenon_Hb8 zenon_Hed zenon_H13c. % 4.69/4.85 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H55 | zenon_intro zenon_H56 ]. % 4.69/4.85 cut (((e3) = (e3)) = ((e1) = (e3))). % 4.69/4.85 intro zenon_D_pnotp. % 4.69/4.85 apply zenon_H13c. % 4.69/4.85 rewrite <- zenon_D_pnotp. % 4.69/4.85 exact zenon_H55. % 4.69/4.85 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H56]. % 4.69/4.85 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H13d]. % 4.69/4.85 congruence. % 4.69/4.85 cut (((op (e0) (e2)) = (e1)) = ((e3) = (e1))). % 4.69/4.85 intro zenon_D_pnotp. % 4.69/4.85 apply zenon_H13d. % 4.69/4.85 rewrite <- zenon_D_pnotp. % 4.69/4.85 exact zenon_Hb8. % 4.69/4.85 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 4.69/4.85 cut (((op (e0) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hee]. % 4.69/4.85 congruence. % 4.69/4.85 exact (zenon_Hee zenon_Hed). % 4.69/4.85 apply zenon_H9b. apply refl_equal. % 4.69/4.85 apply zenon_H56. apply refl_equal. % 4.69/4.85 apply zenon_H56. apply refl_equal. % 4.69/4.85 (* end of lemma zenon_L144_ *) % 4.69/4.85 assert (zenon_L145_ : (~((op (e0) (op (e0) (e0))) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e2)) -> False). % 4.69/4.85 do 0 intro. intros zenon_H189 zenon_Hb6. % 4.69/4.85 cut (((op (e0) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hb4]. % 4.69/4.85 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 4.69/4.85 congruence. % 4.69/4.85 apply zenon_H52. apply refl_equal. % 4.69/4.85 exact (zenon_Hb4 zenon_Hb6). % 4.69/4.85 (* end of lemma zenon_L145_ *) % 4.69/4.85 assert (zenon_L146_ : ((op (e1) (e2)) = (e3)) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> False). % 4.69/4.85 do 0 intro. intros zenon_H162 zenon_Hb8 zenon_Hb6. % 4.69/4.85 apply (zenon_notand_s _ _ ax15); [ zenon_intro zenon_H126 | zenon_intro zenon_H18a ]. % 4.69/4.85 elim (classic ((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 4.69/4.85 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0)))) = ((e1) = (op (e0) (op (e0) (e0))))). % 4.69/4.85 intro zenon_D_pnotp. % 4.69/4.85 apply zenon_H126. % 4.69/4.85 rewrite <- zenon_D_pnotp. % 4.69/4.85 exact zenon_H61. % 4.69/4.85 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 4.69/4.85 cut (((op (e0) (op (e0) (e0))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H127]. % 4.69/4.85 congruence. % 4.69/4.85 cut (((op (e0) (e2)) = (e1)) = ((op (e0) (op (e0) (e0))) = (e1))). % 4.69/4.85 intro zenon_D_pnotp. % 4.69/4.85 apply zenon_H127. % 4.69/4.85 rewrite <- zenon_D_pnotp. % 4.69/4.85 exact zenon_Hb8. % 4.69/4.85 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 4.69/4.85 cut (((op (e0) (e2)) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H18b]. % 4.69/4.85 congruence. % 4.69/4.85 elim (classic ((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 4.69/4.85 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0)))) = ((op (e0) (e2)) = (op (e0) (op (e0) (e0))))). % 4.69/4.85 intro zenon_D_pnotp. % 4.69/4.85 apply zenon_H18b. % 4.69/4.85 rewrite <- zenon_D_pnotp. % 4.69/4.85 exact zenon_H61. % 4.69/4.85 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 4.69/4.85 cut (((op (e0) (op (e0) (e0))) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H189]. % 4.69/4.85 congruence. % 4.69/4.85 apply (zenon_L145_); trivial. % 4.69/4.85 apply zenon_H62. apply refl_equal. % 4.69/4.85 apply zenon_H62. apply refl_equal. % 4.69/4.85 apply zenon_H9b. apply refl_equal. % 4.69/4.85 apply zenon_H62. apply refl_equal. % 4.69/4.85 apply zenon_H62. apply refl_equal. % 4.69/4.85 apply (zenon_notand_s _ _ zenon_H18a); [ zenon_intro zenon_H18c | zenon_intro zenon_H65 ]. % 4.69/4.85 apply zenon_H18c. apply sym_equal. exact zenon_Hb6. % 4.69/4.85 elim (classic ((op (op (e0) (op (e0) (e0))) (op (e0) (e0))) = (op (op (e0) (op (e0) (e0))) (op (e0) (e0))))); [ zenon_intro zenon_H67 | zenon_intro zenon_H68 ]. % 4.69/4.85 cut (((op (op (e0) (op (e0) (e0))) (op (e0) (e0))) = (op (op (e0) (op (e0) (e0))) (op (e0) (e0)))) = ((e3) = (op (op (e0) (op (e0) (e0))) (op (e0) (e0))))). % 4.69/4.85 intro zenon_D_pnotp. % 4.69/4.85 apply zenon_H65. % 4.69/4.85 rewrite <- zenon_D_pnotp. % 4.69/4.85 exact zenon_H67. % 4.69/4.85 cut (((op (op (e0) (op (e0) (e0))) (op (e0) (e0))) = (op (op (e0) (op (e0) (e0))) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H68]. % 4.69/4.85 cut (((op (op (e0) (op (e0) (e0))) (op (e0) (e0))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 4.69/4.85 congruence. % 4.69/4.85 cut (((op (e1) (e2)) = (e3)) = ((op (op (e0) (op (e0) (e0))) (op (e0) (e0))) = (e3))). % 4.69/4.85 intro zenon_D_pnotp. % 4.69/4.85 apply zenon_H69. % 4.69/4.85 rewrite <- zenon_D_pnotp. % 4.69/4.85 exact zenon_H162. % 4.69/4.85 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H56]. % 4.69/4.85 cut (((op (e1) (e2)) = (op (op (e0) (op (e0) (e0))) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H18d]. % 4.69/4.85 congruence. % 4.69/4.85 elim (classic ((op (op (e0) (op (e0) (e0))) (op (e0) (e0))) = (op (op (e0) (op (e0) (e0))) (op (e0) (e0))))); [ zenon_intro zenon_H67 | zenon_intro zenon_H68 ]. % 4.69/4.85 cut (((op (op (e0) (op (e0) (e0))) (op (e0) (e0))) = (op (op (e0) (op (e0) (e0))) (op (e0) (e0)))) = ((op (e1) (e2)) = (op (op (e0) (op (e0) (e0))) (op (e0) (e0))))). % 4.69/4.85 intro zenon_D_pnotp. % 4.69/4.85 apply zenon_H18d. % 4.69/4.85 rewrite <- zenon_D_pnotp. % 4.69/4.85 exact zenon_H67. % 4.69/4.85 cut (((op (op (e0) (op (e0) (e0))) (op (e0) (e0))) = (op (op (e0) (op (e0) (e0))) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H68]. % 4.69/4.85 cut (((op (op (e0) (op (e0) (e0))) (op (e0) (e0))) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H18e]. % 4.69/4.85 congruence. % 4.69/4.85 cut (((op (e0) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hb4]. % 4.69/4.85 cut (((op (e0) (op (e0) (e0))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H127]. % 4.69/4.85 congruence. % 4.69/4.85 cut (((op (e0) (e2)) = (e1)) = ((op (e0) (op (e0) (e0))) = (e1))). % 4.69/4.85 intro zenon_D_pnotp. % 4.69/4.85 apply zenon_H127. % 4.69/4.85 rewrite <- zenon_D_pnotp. % 4.69/4.85 exact zenon_Hb8. % 4.69/4.85 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 4.69/4.85 cut (((op (e0) (e2)) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H18b]. % 4.69/4.85 congruence. % 4.69/4.85 elim (classic ((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 4.69/4.85 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0)))) = ((op (e0) (e2)) = (op (e0) (op (e0) (e0))))). % 4.69/4.85 intro zenon_D_pnotp. % 4.69/4.85 apply zenon_H18b. % 4.69/4.85 rewrite <- zenon_D_pnotp. % 4.69/4.85 exact zenon_H61. % 4.69/4.85 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 4.69/4.85 cut (((op (e0) (op (e0) (e0))) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H189]. % 4.69/4.85 congruence. % 4.69/4.85 apply (zenon_L145_); trivial. % 4.69/4.85 apply zenon_H62. apply refl_equal. % 4.69/4.85 apply zenon_H62. apply refl_equal. % 4.69/4.85 apply zenon_H9b. apply refl_equal. % 4.69/4.85 exact (zenon_Hb4 zenon_Hb6). % 4.69/4.85 apply zenon_H68. apply refl_equal. % 4.69/4.85 apply zenon_H68. apply refl_equal. % 4.69/4.85 apply zenon_H56. apply refl_equal. % 4.69/4.85 apply zenon_H68. apply refl_equal. % 4.69/4.85 apply zenon_H68. apply refl_equal. % 4.69/4.85 (* end of lemma zenon_L146_ *) % 4.69/4.85 assert (zenon_L147_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e2)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> False). % 4.69/4.85 do 0 intro. intros zenon_H18f zenon_H13c zenon_Hb6 zenon_Hb8 zenon_H4d zenon_H2b. % 4.69/4.85 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_Hed | zenon_intro zenon_H190 ]. % 4.69/4.85 apply (zenon_L144_); trivial. % 4.69/4.85 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H162 | zenon_intro zenon_H191 ]. % 4.69/4.85 apply (zenon_L146_); trivial. % 4.69/4.85 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_H50 | zenon_intro zenon_H32 ]. % 4.69/4.85 exact (zenon_H4d zenon_H50). % 4.69/4.85 exact (zenon_H2b zenon_H32). % 4.69/4.85 (* end of lemma zenon_L147_ *) % 4.69/4.85 assert (zenon_L148_ : ((op (e0) (e1)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> (~((e0) = (e2))) -> False). % 4.69/4.85 do 0 intro. intros zenon_H25 zenon_H5e zenon_H82. % 4.69/4.85 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H83 | zenon_intro zenon_H5c ]. % 4.69/4.85 cut (((e2) = (e2)) = ((e0) = (e2))). % 4.69/4.85 intro zenon_D_pnotp. % 4.69/4.85 apply zenon_H82. % 4.69/4.85 rewrite <- zenon_D_pnotp. % 4.69/4.85 exact zenon_H83. % 4.69/4.85 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 4.69/4.85 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 4.69/4.85 congruence. % 4.69/4.85 cut (((op (e0) (e1)) = (e0)) = ((e2) = (e0))). % 4.69/4.85 intro zenon_D_pnotp. % 4.69/4.85 apply zenon_H84. % 4.69/4.85 rewrite <- zenon_D_pnotp. % 4.69/4.85 exact zenon_H25. % 4.69/4.85 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 4.69/4.85 cut (((op (e0) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H9f]. % 4.69/4.85 congruence. % 4.69/4.85 exact (zenon_H9f zenon_H5e). % 4.69/4.85 apply zenon_H52. apply refl_equal. % 4.69/4.85 apply zenon_H5c. apply refl_equal. % 4.69/4.85 apply zenon_H5c. apply refl_equal. % 4.69/4.85 (* end of lemma zenon_L148_ *) % 4.69/4.85 assert (zenon_L149_ : ((op (e0) (e2)) = (e1)) -> ((op (e0) (e2)) = (e2)) -> (~((e1) = (e2))) -> False). % 4.69/4.85 do 0 intro. intros zenon_Hb8 zenon_H92 zenon_H9d. % 4.69/4.85 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H83 | zenon_intro zenon_H5c ]. % 4.69/4.85 cut (((e2) = (e2)) = ((e1) = (e2))). % 4.69/4.85 intro zenon_D_pnotp. % 4.69/4.85 apply zenon_H9d. % 4.69/4.85 rewrite <- zenon_D_pnotp. % 4.69/4.85 exact zenon_H83. % 4.69/4.85 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 4.69/4.85 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9e]. % 4.69/4.85 congruence. % 4.69/4.85 cut (((op (e0) (e2)) = (e1)) = ((e2) = (e1))). % 4.69/4.85 intro zenon_D_pnotp. % 4.69/4.85 apply zenon_H9e. % 4.69/4.85 rewrite <- zenon_D_pnotp. % 4.69/4.85 exact zenon_Hb8. % 4.69/4.85 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 4.69/4.85 cut (((op (e0) (e2)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H93]. % 4.69/4.85 congruence. % 4.69/4.85 exact (zenon_H93 zenon_H92). % 4.69/4.85 apply zenon_H9b. apply refl_equal. % 4.69/4.85 apply zenon_H5c. apply refl_equal. % 4.69/4.85 apply zenon_H5c. apply refl_equal. % 4.69/4.85 (* end of lemma zenon_L149_ *) % 4.69/4.85 assert (zenon_L150_ : (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> False). % 4.69/4.85 do 0 intro. intros zenon_Hf6 zenon_H123 zenon_H192. % 4.69/4.85 cut (((op (e3) (e0)) = (e1)) = ((op (e3) (e0)) = (op (e3) (e2)))). % 4.69/4.85 intro zenon_D_pnotp. % 4.69/4.85 apply zenon_Hf6. % 4.69/4.85 rewrite <- zenon_D_pnotp. % 4.69/4.85 exact zenon_H123. % 4.69/4.85 cut (((e1) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H193]. % 4.69/4.85 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 4.69/4.85 congruence. % 4.69/4.85 apply zenon_Hb2. apply refl_equal. % 4.69/4.85 apply zenon_H193. apply sym_equal. exact zenon_H192. % 4.69/4.85 (* end of lemma zenon_L150_ *) % 4.69/4.85 assert (zenon_L151_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e1)) -> False). % 4.69/4.85 do 0 intro. intros zenon_H194 zenon_H13c zenon_Hed zenon_H195 zenon_H16c zenon_Hf6 zenon_H123. % 4.69/4.85 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H196 ]. % 4.69/4.85 apply (zenon_L144_); trivial. % 4.69/4.85 apply (zenon_or_s _ _ zenon_H196); [ zenon_intro zenon_H47 | zenon_intro zenon_H197 ]. % 4.69/4.85 exact (zenon_H195 zenon_H47). % 4.69/4.85 apply (zenon_or_s _ _ zenon_H197); [ zenon_intro zenon_H48 | zenon_intro zenon_H192 ]. % 4.69/4.85 exact (zenon_H16c zenon_H48). % 4.69/4.85 apply (zenon_L150_); trivial. % 4.69/4.85 (* end of lemma zenon_L151_ *) % 4.69/4.85 assert (zenon_L152_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 4.69/4.85 do 0 intro. intros zenon_H103 zenon_H104 zenon_H54 zenon_H25 zenon_H123 zenon_Hf6 zenon_H16c zenon_H195 zenon_H13c zenon_H194 zenon_H8a zenon_Hfd. % 4.69/4.85 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_H108 | zenon_intro zenon_H107 ]. % 4.69/4.85 exact (zenon_H104 zenon_H108). % 4.69/4.85 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H109 ]. % 4.69/4.85 apply (zenon_L94_); trivial. % 4.69/4.85 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Hed | zenon_intro zenon_H8c ]. % 4.69/4.85 apply (zenon_L151_); trivial. % 4.69/4.85 apply (zenon_L115_); trivial. % 4.69/4.85 (* end of lemma zenon_L152_ *) % 4.69/4.85 assert (zenon_L153_ : ((op (e3) (e1)) = (e1)) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> False). % 4.69/4.85 do 0 intro. intros zenon_Hfa zenon_H30 zenon_H13c. % 4.69/4.85 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H55 | zenon_intro zenon_H56 ]. % 4.69/4.85 cut (((e3) = (e3)) = ((e1) = (e3))). % 4.69/4.85 intro zenon_D_pnotp. % 4.69/4.85 apply zenon_H13c. % 4.69/4.85 rewrite <- zenon_D_pnotp. % 4.69/4.85 exact zenon_H55. % 4.69/4.85 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H56]. % 4.69/4.85 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H13d]. % 4.69/4.85 congruence. % 4.69/4.85 cut (((op (e3) (e1)) = (e1)) = ((e3) = (e1))). % 4.69/4.85 intro zenon_D_pnotp. % 4.69/4.85 apply zenon_H13d. % 4.69/4.85 rewrite <- zenon_D_pnotp. % 4.69/4.85 exact zenon_Hfa. % 4.69/4.85 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 4.69/4.85 cut (((op (e3) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2a]. % 4.69/4.85 congruence. % 4.69/4.85 exact (zenon_H2a zenon_H30). % 4.69/4.85 apply zenon_H9b. apply refl_equal. % 4.69/4.85 apply zenon_H56. apply refl_equal. % 4.69/4.85 apply zenon_H56. apply refl_equal. % 4.69/4.85 (* end of lemma zenon_L153_ *) % 4.69/4.85 assert (zenon_L154_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (~((e1) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> False). % 4.69/4.85 do 0 intro. intros zenon_H101 zenon_Hb9 zenon_H25 zenon_H36 zenon_Hf0 zenon_Hef zenon_H28 zenon_H29 zenon_H13c zenon_H2b zenon_H2c. % 4.69/4.85 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H9c | zenon_intro zenon_H10a ]. % 4.69/4.85 apply (zenon_L92_); trivial. % 4.69/4.85 apply (zenon_or_s _ _ zenon_H10a); [ zenon_intro zenon_H3e | zenon_intro zenon_H10b ]. % 4.69/4.85 exact (zenon_H36 zenon_H3e). % 4.69/4.85 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hfa ]. % 4.69/4.85 apply (zenon_L54_); trivial. % 4.69/4.85 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2e | zenon_intro zenon_H2d ]. % 4.69/4.85 exact (zenon_H29 zenon_H2e). % 4.69/4.85 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H30 | zenon_intro zenon_H2f ]. % 4.69/4.85 apply (zenon_L153_); trivial. % 4.69/4.85 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 4.69/4.85 exact (zenon_H2b zenon_H32). % 4.69/4.85 exact (zenon_H2c zenon_H31). % 4.69/4.85 (* end of lemma zenon_L154_ *) % 4.69/4.85 assert (zenon_L155_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> False). % 4.69/4.85 do 0 intro. intros zenon_H28 zenon_H29 zenon_Hd1 zenon_H198 zenon_H2b zenon_H2c. % 4.69/4.85 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2e | zenon_intro zenon_H2d ]. % 4.69/4.85 exact (zenon_H29 zenon_H2e). % 4.69/4.85 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H30 | zenon_intro zenon_H2f ]. % 4.69/4.85 cut (((op (e0) (e1)) = (e3)) = ((op (e0) (e1)) = (op (e3) (e1)))). % 4.69/4.85 intro zenon_D_pnotp. % 4.69/4.85 apply zenon_H198. % 4.69/4.85 rewrite <- zenon_D_pnotp. % 4.69/4.85 exact zenon_Hd1. % 4.69/4.85 cut (((e3) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H199]. % 4.69/4.85 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hd3]. % 4.69/4.85 congruence. % 4.69/4.85 apply zenon_Hd3. apply refl_equal. % 4.69/4.85 apply zenon_H199. apply sym_equal. exact zenon_H30. % 4.69/4.85 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 4.69/4.85 exact (zenon_H2b zenon_H32). % 4.69/4.85 exact (zenon_H2c zenon_H31). % 4.69/4.85 (* end of lemma zenon_L155_ *) % 4.69/4.85 assert (zenon_L156_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 4.69/4.85 do 0 intro. intros zenon_H103 zenon_H104 zenon_H2c zenon_H2b zenon_H198 zenon_H29 zenon_H28 zenon_H123 zenon_Hf6 zenon_H16c zenon_H195 zenon_H194 zenon_H87 zenon_H13c. % 4.69/4.85 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_H108 | zenon_intro zenon_H107 ]. % 4.69/4.85 exact (zenon_H104 zenon_H108). % 4.69/4.85 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H109 ]. % 4.69/4.85 apply (zenon_L155_); trivial. % 4.69/4.85 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Hed | zenon_intro zenon_H8c ]. % 4.69/4.85 apply (zenon_L151_); trivial. % 4.69/4.85 apply (zenon_L95_); trivial. % 4.69/4.85 (* end of lemma zenon_L156_ *) % 4.69/4.85 assert (zenon_L157_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 4.69/4.85 do 0 intro. intros zenon_H137 zenon_H5b zenon_H7c zenon_Hef zenon_H36 zenon_H25 zenon_Hb9 zenon_H101 zenon_H103 zenon_H104 zenon_H2c zenon_H2b zenon_H198 zenon_H29 zenon_H28 zenon_Hf6 zenon_H16c zenon_H195 zenon_H194 zenon_H87 zenon_H13c. % 4.69/4.85 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_H5a | zenon_intro zenon_H138 ]. % 4.69/4.85 exact (zenon_H5b zenon_H5a). % 4.69/4.85 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_H7e | zenon_intro zenon_H139 ]. % 4.69/4.85 exact (zenon_H7c zenon_H7e). % 4.69/4.85 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H123 ]. % 4.69/4.85 apply (zenon_L154_); trivial. % 4.69/4.85 apply (zenon_L156_); trivial. % 4.69/4.85 (* end of lemma zenon_L157_ *) % 4.69/4.85 assert (zenon_L158_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 4.69/4.85 do 0 intro. intros zenon_H103 zenon_H104 zenon_H2c zenon_H2b zenon_H198 zenon_H29 zenon_H28 zenon_H123 zenon_Hf6 zenon_H16c zenon_H195 zenon_H13c zenon_H194 zenon_H26 zenon_H54. % 4.69/4.85 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_H108 | zenon_intro zenon_H107 ]. % 4.69/4.85 exact (zenon_H104 zenon_H108). % 4.69/4.85 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H109 ]. % 4.69/4.85 apply (zenon_L155_); trivial. % 4.69/4.85 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Hed | zenon_intro zenon_H8c ]. % 4.69/4.85 apply (zenon_L151_); trivial. % 4.69/4.85 apply (zenon_L60_); trivial. % 4.69/4.85 (* end of lemma zenon_L158_ *) % 4.69/4.85 assert (zenon_L159_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e3))) -> False). % 4.69/4.85 do 0 intro. intros zenon_H1d zenon_H1e zenon_H101 zenon_Hb9 zenon_H36 zenon_Hef zenon_H100 zenon_H18f zenon_H82 zenon_H9d zenon_Hfd zenon_H118 zenon_H20 zenon_H137 zenon_H5b zenon_H7c zenon_H4b zenon_H4c zenon_H4d zenon_H186 zenon_H103 zenon_H104 zenon_H2c zenon_H2b zenon_H198 zenon_H29 zenon_H28 zenon_Hf6 zenon_H16c zenon_H195 zenon_H13c zenon_H194 zenon_H54. % 4.69/4.85 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ]. % 4.69/4.85 exact (zenon_H1e zenon_H23). % 4.69/4.85 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ]. % 4.69/4.85 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H5a | zenon_intro zenon_H119 ]. % 4.69/4.85 exact (zenon_H5b zenon_H5a). % 4.69/4.85 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H9c | zenon_intro zenon_H11c ]. % 4.69/4.85 apply (zenon_L92_); trivial. % 4.69/4.85 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H87 ]. % 4.69/4.85 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_H5a | zenon_intro zenon_H138 ]. % 4.69/4.85 exact (zenon_H5b zenon_H5a). % 4.69/4.85 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_H7e | zenon_intro zenon_H139 ]. % 4.69/4.85 exact (zenon_H7c zenon_H7e). % 4.69/4.85 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H123 ]. % 4.69/4.85 apply (zenon_L143_); trivial. % 4.69/4.85 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hb6 | zenon_intro zenon_H105 ]. % 4.69/4.85 apply (zenon_L147_); trivial. % 4.69/4.85 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H5e | zenon_intro zenon_H106 ]. % 4.69/4.85 apply (zenon_L148_); trivial. % 4.69/4.85 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_H92 | zenon_intro zenon_H8a ]. % 4.69/4.85 apply (zenon_L149_); trivial. % 4.69/4.85 apply (zenon_L152_); trivial. % 4.69/4.85 apply (zenon_L157_); trivial. % 4.69/4.85 apply (zenon_or_s _ _ zenon_H24); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 4.69/4.85 exact (zenon_H20 zenon_H27). % 4.69/4.85 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_H5a | zenon_intro zenon_H138 ]. % 4.69/4.85 exact (zenon_H5b zenon_H5a). % 4.69/4.85 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_H7e | zenon_intro zenon_H139 ]. % 4.69/4.85 exact (zenon_H7c zenon_H7e). % 4.69/4.85 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H123 ]. % 4.69/4.85 apply (zenon_L143_); trivial. % 4.69/4.85 apply (zenon_L158_); trivial. % 4.69/4.85 (* end of lemma zenon_L159_ *) % 4.69/4.85 assert (zenon_L160_ : ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (~((e1) = (e3))) -> (~((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 (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (e1))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 4.69/4.85 do 0 intro. intros zenon_H19a zenon_H11f zenon_H1e zenon_H118 zenon_H101 zenon_H2c zenon_H28 zenon_Hef zenon_H36 zenon_H198 zenon_H7c zenon_H186 zenon_H29 zenon_H13c zenon_H16c zenon_H4c zenon_H4d zenon_H4b zenon_H104 zenon_H100 zenon_H54 zenon_H194 zenon_Hf6 zenon_H195 zenon_Hfd zenon_H103 zenon_H9d zenon_H82 zenon_H18f zenon_H137 zenon_Hb9 zenon_H5b zenon_H20 zenon_H1d. % 4.69/4.85 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H2b | zenon_intro zenon_Hb4 ]. % 4.69/4.85 apply (zenon_L159_); trivial. % 4.69/4.85 apply (zenon_L73_); trivial. % 4.69/4.85 (* end of lemma zenon_L160_ *) % 4.69/4.85 assert (zenon_L161_ : ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (e3))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (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))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (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 (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> False). % 4.69/4.85 do 0 intro. intros zenon_H19b zenon_H20 zenon_H18f zenon_H195 zenon_Hf6 zenon_H194 zenon_H104 zenon_H4b zenon_H4d zenon_H4c zenon_H186 zenon_H7c zenon_H198 zenon_Hef zenon_H101 zenon_H28 zenon_H2c zenon_H29 zenon_H175 zenon_H176 zenon_H174 zenon_H173 zenon_H172 zenon_H16f zenon_H16b zenon_He9 zenon_H166 zenon_H86 zenon_H165 zenon_Hbe zenon_H170 zenon_H152 zenon_H114 zenon_H7b zenon_H132 zenon_H36 zenon_H100 zenon_Hd0 zenon_H94 zenon_H137 zenon_Hac zenon_H82 zenon_Ha0 zenon_Ha4 zenon_Ha9 zenon_H9d zenon_Haf zenon_Hb3 zenon_Hb9 zenon_H12e zenon_H118 zenon_Hdf zenon_H13e zenon_H117 zenon_H142 zenon_H70 zenon_H75 zenon_H113 zenon_H54 zenon_Hfd zenon_H13c zenon_H103 zenon_H153 zenon_H154 zenon_H171 zenon_H177 zenon_H1d zenon_H1f zenon_H1e zenon_H11f zenon_H5b zenon_H122 zenon_H19a. % 4.69/4.85 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H2a | zenon_intro zenon_H16c ]. % 4.69/4.85 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H2b | zenon_intro zenon_Hb4 ]. % 4.69/4.85 apply (zenon_L2_); trivial. % 4.69/4.85 apply (zenon_L138_); trivial. % 4.69/4.85 apply (zenon_L160_); trivial. % 4.69/4.85 (* end of lemma zenon_L161_ *) % 4.69/4.85 assert (zenon_L162_ : ((~((op (e3) (e1)) = (e3)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (~((e1) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (e0))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (((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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (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 (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> False). % 4.69/4.85 do 0 intro. intros zenon_H19c zenon_H122 zenon_H11f zenon_H177 zenon_H171 zenon_H154 zenon_H153 zenon_H13c zenon_H142 zenon_H13e zenon_H12e zenon_H137 zenon_H132 zenon_H152 zenon_H170 zenon_H165 zenon_H166 zenon_H16b zenon_H16f zenon_H172 zenon_H173 zenon_H174 zenon_H176 zenon_H175 zenon_H198 zenon_H186 zenon_H194 zenon_H195 zenon_H18f zenon_H20 zenon_H19b zenon_H28 zenon_H2c zenon_H29 zenon_H11e zenon_H1d zenon_H33 zenon_H38 zenon_H36 zenon_H35 zenon_H118 zenon_Hb9 zenon_Hac zenon_Ha0 zenon_Ha4 zenon_Ha9 zenon_H9d zenon_Haf zenon_Hb3 zenon_H95 zenon_H96 zenon_He2 zenon_H75 zenon_H70 zenon_H6c zenon_H7b zenon_H82 zenon_H8f zenon_H89 zenon_H86 zenon_H117 zenon_H54 zenon_H94 zenon_H41 zenon_H46 zenon_H4c zenon_H4d zenon_H4b zenon_H7c zenon_H100 zenon_Hfd zenon_H103 zenon_H101 zenon_Hf9 zenon_Hf3 zenon_Hef zenon_Hf6 zenon_H102 zenon_Hbe zenon_Hd0 zenon_Hdf zenon_Hd7 zenon_Hda zenon_Hdc zenon_He6 zenon_He9 zenon_H104 zenon_H110 zenon_H113 zenon_H114 zenon_H1f zenon_H1e zenon_H11d zenon_H19a. % 4.69/4.85 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H2a | zenon_intro zenon_H5b ]. % 4.69/4.85 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H2b | zenon_intro zenon_Hb4 ]. % 4.69/4.85 apply (zenon_L2_); trivial. % 4.69/4.85 apply (zenon_L72_); trivial. % 4.69/4.85 apply (zenon_L161_); trivial. % 4.69/4.85 (* end of lemma zenon_L162_ *) % 4.69/4.85 assert (zenon_L163_ : ((op (e0) (e0)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (~((e1) = (e2))) -> False). % 4.69/4.85 do 0 intro. intros zenon_H5a zenon_Hb6 zenon_H9d. % 4.69/4.85 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H83 | zenon_intro zenon_H5c ]. % 4.69/4.85 cut (((e2) = (e2)) = ((e1) = (e2))). % 4.69/4.85 intro zenon_D_pnotp. % 4.69/4.85 apply zenon_H9d. % 4.69/4.85 rewrite <- zenon_D_pnotp. % 4.69/4.85 exact zenon_H83. % 4.69/4.85 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 4.69/4.85 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9e]. % 4.69/4.85 congruence. % 4.69/4.85 cut (((op (e0) (e0)) = (e1)) = ((e2) = (e1))). % 4.69/4.85 intro zenon_D_pnotp. % 4.69/4.85 apply zenon_H9e. % 4.69/4.85 rewrite <- zenon_D_pnotp. % 4.69/4.85 exact zenon_H5a. % 4.69/4.85 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 4.69/4.85 cut (((op (e0) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hb4]. % 4.69/4.85 congruence. % 4.69/4.85 exact (zenon_Hb4 zenon_Hb6). % 4.69/4.85 apply zenon_H9b. apply refl_equal. % 4.69/4.85 apply zenon_H5c. apply refl_equal. % 4.69/4.85 apply zenon_H5c. apply refl_equal. % 4.69/4.85 (* end of lemma zenon_L163_ *) % 4.69/4.85 assert (zenon_L164_ : (((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). % 4.69/4.85 do 0 intro. intros zenon_H33 zenon_Hc3 zenon_H36 zenon_H5e zenon_H19d zenon_H38. % 4.69/4.85 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H3a | zenon_intro zenon_H39 ]. % 4.69/4.85 exact (zenon_Hc3 zenon_H3a). % 4.69/4.85 apply (zenon_or_s _ _ zenon_H39); [ zenon_intro zenon_H3e | zenon_intro zenon_H3d ]. % 4.69/4.85 exact (zenon_H36 zenon_H3e). % 4.69/4.85 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H40 | zenon_intro zenon_H3f ]. % 4.69/4.85 cut (((op (e0) (e1)) = (e2)) = ((op (e0) (e1)) = (op (e1) (e1)))). % 4.69/4.85 intro zenon_D_pnotp. % 4.69/4.85 apply zenon_H19d. % 4.69/4.85 rewrite <- zenon_D_pnotp. % 4.69/4.85 exact zenon_H5e. % 4.69/4.85 cut (((e2) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H19e]. % 4.69/4.85 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hd3]. % 4.69/4.85 congruence. % 4.69/4.85 apply zenon_Hd3. apply refl_equal. % 4.69/4.85 apply zenon_H19e. apply sym_equal. exact zenon_H40. % 4.69/4.85 exact (zenon_H38 zenon_H3f). % 4.69/4.85 (* end of lemma zenon_L164_ *) % 4.69/4.85 assert (zenon_L165_ : (~((op (e2) (op (e2) (e2))) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e1)) -> False). % 4.69/4.85 do 0 intro. intros zenon_H19f zenon_H48. % 4.69/4.85 cut (((op (e2) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H16c]. % 4.69/4.86 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 4.69/4.86 congruence. % 4.69/4.86 apply zenon_H5c. apply refl_equal. % 4.69/4.86 exact (zenon_H16c zenon_H48). % 4.69/4.86 (* end of lemma zenon_L165_ *) % 4.69/4.86 assert (zenon_L166_ : (~((op (op (e2) (op (e2) (e2))) (op (e2) (e2))) = (op (e0) (e1)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e2) (e1)) = (e0)) -> False). % 4.69/4.86 do 0 intro. intros zenon_H1a0 zenon_H48 zenon_H1a1. % 4.69/4.86 cut (((op (e2) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H16c]. % 4.69/4.86 cut (((op (e2) (op (e2) (e2))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1a2]. % 4.69/4.86 congruence. % 4.69/4.86 cut (((op (e2) (e1)) = (e0)) = ((op (e2) (op (e2) (e2))) = (e0))). % 4.69/4.86 intro zenon_D_pnotp. % 4.69/4.86 apply zenon_H1a2. % 4.69/4.86 rewrite <- zenon_D_pnotp. % 4.69/4.86 exact zenon_H1a1. % 4.69/4.86 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 4.69/4.86 cut (((op (e2) (e1)) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H1a3]. % 4.69/4.86 congruence. % 4.69/4.86 elim (classic ((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [ zenon_intro zenon_H17d | zenon_intro zenon_H17e ]. % 4.69/4.86 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2)))) = ((op (e2) (e1)) = (op (e2) (op (e2) (e2))))). % 4.69/4.86 intro zenon_D_pnotp. % 4.69/4.86 apply zenon_H1a3. % 4.69/4.86 rewrite <- zenon_D_pnotp. % 4.69/4.86 exact zenon_H17d. % 4.69/4.86 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H17e]. % 4.69/4.86 cut (((op (e2) (op (e2) (e2))) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H19f]. % 4.69/4.86 congruence. % 4.69/4.86 apply (zenon_L165_); trivial. % 4.69/4.86 apply zenon_H17e. apply refl_equal. % 4.69/4.86 apply zenon_H17e. apply refl_equal. % 4.69/4.86 apply zenon_H52. apply refl_equal. % 4.69/4.86 exact (zenon_H16c zenon_H48). % 4.69/4.86 (* end of lemma zenon_L166_ *) % 4.69/4.86 assert (zenon_L167_ : ((op (e0) (e1)) = (e3)) -> ((op (e2) (e1)) = (e0)) -> ((op (e2) (e2)) = (e1)) -> False). % 4.69/4.86 do 0 intro. intros zenon_Hd1 zenon_H1a1 zenon_H48. % 4.69/4.86 apply (zenon_notand_s _ _ ax7); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H1a4 ]. % 4.69/4.86 elim (classic ((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [ zenon_intro zenon_H17d | zenon_intro zenon_H17e ]. % 4.69/4.86 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2)))) = ((e0) = (op (e2) (op (e2) (e2))))). % 4.69/4.86 intro zenon_D_pnotp. % 4.69/4.86 apply zenon_H1a5. % 4.69/4.86 rewrite <- zenon_D_pnotp. % 4.69/4.86 exact zenon_H17d. % 4.69/4.86 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H17e]. % 4.69/4.86 cut (((op (e2) (op (e2) (e2))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1a2]. % 4.69/4.86 congruence. % 4.69/4.86 cut (((op (e2) (e1)) = (e0)) = ((op (e2) (op (e2) (e2))) = (e0))). % 4.69/4.86 intro zenon_D_pnotp. % 4.69/4.86 apply zenon_H1a2. % 4.69/4.86 rewrite <- zenon_D_pnotp. % 4.69/4.86 exact zenon_H1a1. % 4.69/4.86 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 4.69/4.86 cut (((op (e2) (e1)) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H1a3]. % 4.69/4.86 congruence. % 4.69/4.86 elim (classic ((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [ zenon_intro zenon_H17d | zenon_intro zenon_H17e ]. % 4.69/4.86 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2)))) = ((op (e2) (e1)) = (op (e2) (op (e2) (e2))))). % 4.69/4.86 intro zenon_D_pnotp. % 4.69/4.86 apply zenon_H1a3. % 4.69/4.86 rewrite <- zenon_D_pnotp. % 4.69/4.86 exact zenon_H17d. % 4.69/4.86 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H17e]. % 4.69/4.86 cut (((op (e2) (op (e2) (e2))) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H19f]. % 4.69/4.86 congruence. % 4.69/4.86 apply (zenon_L165_); trivial. % 4.69/4.86 apply zenon_H17e. apply refl_equal. % 4.69/4.86 apply zenon_H17e. apply refl_equal. % 4.69/4.86 apply zenon_H52. apply refl_equal. % 4.69/4.86 apply zenon_H17e. apply refl_equal. % 4.69/4.86 apply zenon_H17e. apply refl_equal. % 4.69/4.86 apply (zenon_notand_s _ _ zenon_H1a4); [ zenon_intro zenon_H49 | zenon_intro zenon_H181 ]. % 4.69/4.86 apply zenon_H49. apply sym_equal. exact zenon_H48. % 4.69/4.86 elim (classic ((op (op (e2) (op (e2) (e2))) (op (e2) (e2))) = (op (op (e2) (op (e2) (e2))) (op (e2) (e2))))); [ zenon_intro zenon_H182 | zenon_intro zenon_H183 ]. % 4.69/4.86 cut (((op (op (e2) (op (e2) (e2))) (op (e2) (e2))) = (op (op (e2) (op (e2) (e2))) (op (e2) (e2)))) = ((e3) = (op (op (e2) (op (e2) (e2))) (op (e2) (e2))))). % 4.69/4.86 intro zenon_D_pnotp. % 4.69/4.86 apply zenon_H181. % 4.69/4.86 rewrite <- zenon_D_pnotp. % 4.69/4.86 exact zenon_H182. % 4.69/4.86 cut (((op (op (e2) (op (e2) (e2))) (op (e2) (e2))) = (op (op (e2) (op (e2) (e2))) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H183]. % 4.69/4.86 cut (((op (op (e2) (op (e2) (e2))) (op (e2) (e2))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H184]. % 4.69/4.86 congruence. % 4.69/4.86 cut (((op (e0) (e1)) = (e3)) = ((op (op (e2) (op (e2) (e2))) (op (e2) (e2))) = (e3))). % 4.69/4.86 intro zenon_D_pnotp. % 4.69/4.86 apply zenon_H184. % 4.69/4.86 rewrite <- zenon_D_pnotp. % 4.69/4.86 exact zenon_Hd1. % 4.69/4.86 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H56]. % 4.69/4.86 cut (((op (e0) (e1)) = (op (op (e2) (op (e2) (e2))) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H1a6]. % 4.69/4.86 congruence. % 4.69/4.86 elim (classic ((op (op (e2) (op (e2) (e2))) (op (e2) (e2))) = (op (op (e2) (op (e2) (e2))) (op (e2) (e2))))); [ zenon_intro zenon_H182 | zenon_intro zenon_H183 ]. % 4.69/4.86 cut (((op (op (e2) (op (e2) (e2))) (op (e2) (e2))) = (op (op (e2) (op (e2) (e2))) (op (e2) (e2)))) = ((op (e0) (e1)) = (op (op (e2) (op (e2) (e2))) (op (e2) (e2))))). % 4.69/4.86 intro zenon_D_pnotp. % 4.69/4.86 apply zenon_H1a6. % 4.69/4.86 rewrite <- zenon_D_pnotp. % 4.69/4.86 exact zenon_H182. % 4.69/4.86 cut (((op (op (e2) (op (e2) (e2))) (op (e2) (e2))) = (op (op (e2) (op (e2) (e2))) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H183]. % 4.69/4.86 cut (((op (op (e2) (op (e2) (e2))) (op (e2) (e2))) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1a0]. % 4.69/4.86 congruence. % 4.69/4.86 apply (zenon_L166_); trivial. % 4.69/4.86 apply zenon_H183. apply refl_equal. % 4.69/4.86 apply zenon_H183. apply refl_equal. % 4.69/4.86 apply zenon_H56. apply refl_equal. % 4.69/4.86 apply zenon_H183. apply refl_equal. % 4.69/4.86 apply zenon_H183. apply refl_equal. % 4.69/4.86 (* end of lemma zenon_L167_ *) % 4.69/4.86 assert (zenon_L168_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e0) (e2)) = (e0))) -> (((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 (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 4.69/4.86 do 0 intro. intros zenon_H103 zenon_H104 zenon_Ha4 zenon_H179 zenon_Ha0 zenon_H34 zenon_H20 zenon_H102 zenon_H4b zenon_H4c zenon_H4d zenon_Hc3 zenon_H1f zenon_H1a7 zenon_Hfd zenon_H92 zenon_H26 zenon_H54. % 4.69/4.86 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_H108 | zenon_intro zenon_H107 ]. % 4.69/4.86 exact (zenon_H104 zenon_H108). % 4.69/4.86 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H109 ]. % 4.69/4.86 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_H25 | zenon_intro zenon_H1a8 ]. % 4.69/4.86 exact (zenon_H1f zenon_H25). % 4.69/4.86 apply (zenon_or_s _ _ zenon_H1a8); [ zenon_intro zenon_H3a | zenon_intro zenon_H1a9 ]. % 4.69/4.86 exact (zenon_Hc3 zenon_H3a). % 4.69/4.86 apply (zenon_or_s _ _ zenon_H1a9); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H10e ]. % 4.69/4.86 apply (zenon_or_s _ _ zenon_H4b); [ zenon_intro zenon_H43 | zenon_intro zenon_H4e ]. % 4.69/4.86 exact (zenon_H179 zenon_H43). % 4.69/4.86 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H48 | zenon_intro zenon_H4f ]. % 4.69/4.86 apply (zenon_L167_); trivial. % 4.69/4.86 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H51 | zenon_intro zenon_H50 ]. % 4.69/4.86 exact (zenon_H4c zenon_H51). % 4.69/4.86 exact (zenon_H4d zenon_H50). % 4.69/4.86 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H27 | zenon_intro zenon_H10c ]. % 4.69/4.86 exact (zenon_H20 zenon_H27). % 4.69/4.86 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_He5 | zenon_intro zenon_H10d ]. % 4.69/4.86 cut (((op (e1) (e0)) = (e0)) = ((op (e1) (e0)) = (op (e1) (e2)))). % 4.69/4.86 intro zenon_D_pnotp. % 4.69/4.86 apply zenon_Ha0. % 4.69/4.86 rewrite <- zenon_D_pnotp. % 4.69/4.86 exact zenon_H34. % 4.69/4.86 cut (((e0) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H155]. % 4.69/4.86 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H3c]. % 4.69/4.86 congruence. % 4.69/4.86 apply zenon_H3c. apply refl_equal. % 4.69/4.86 apply zenon_H155. apply sym_equal. exact zenon_He5. % 4.69/4.86 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H43 | zenon_intro zenon_Hf7 ]. % 4.69/4.86 exact (zenon_H179 zenon_H43). % 4.69/4.86 cut (((op (e3) (e1)) = (e0)) = ((op (e3) (e1)) = (op (e3) (e2)))). % 4.69/4.86 intro zenon_D_pnotp. % 4.69/4.86 apply zenon_Ha4. % 4.69/4.86 rewrite <- zenon_D_pnotp. % 4.69/4.86 exact zenon_H10e. % 4.69/4.86 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hf8]. % 4.69/4.86 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Ha8]. % 4.69/4.86 congruence. % 4.69/4.86 apply zenon_Ha8. apply refl_equal. % 4.69/4.86 apply zenon_Hf8. apply sym_equal. exact zenon_Hf7. % 4.69/4.86 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Hed | zenon_intro zenon_H8c ]. % 4.69/4.86 apply (zenon_L62_); trivial. % 4.69/4.86 apply (zenon_L60_); trivial. % 4.69/4.86 (* end of lemma zenon_L168_ *) % 4.69/4.86 assert (zenon_L169_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 4.69/4.86 do 0 intro. intros zenon_H103 zenon_H104 zenon_H13c zenon_H9c zenon_Hfd zenon_H92 zenon_H26 zenon_H54. % 4.69/4.86 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_H108 | zenon_intro zenon_H107 ]. % 4.69/4.86 exact (zenon_H104 zenon_H108). % 4.69/4.86 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H109 ]. % 4.69/4.86 apply (zenon_L114_); trivial. % 4.69/4.86 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Hed | zenon_intro zenon_H8c ]. % 4.69/4.86 apply (zenon_L62_); trivial. % 4.69/4.86 apply (zenon_L60_); trivial. % 4.69/4.86 (* end of lemma zenon_L169_ *) % 4.69/4.86 assert (zenon_L170_ : (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (e2)) = (e1)) -> False). % 4.69/4.86 do 0 intro. intros zenon_H41 zenon_Hf0 zenon_H48. % 4.69/4.86 cut (((op (e2) (e0)) = (e1)) = ((op (e2) (e0)) = (op (e2) (e2)))). % 4.69/4.86 intro zenon_D_pnotp. % 4.69/4.86 apply zenon_H41. % 4.69/4.86 rewrite <- zenon_D_pnotp. % 4.69/4.86 exact zenon_Hf0. % 4.69/4.86 cut (((e1) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H49]. % 4.69/4.86 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H45]. % 4.69/4.86 congruence. % 4.69/4.86 apply zenon_H45. apply refl_equal. % 4.69/4.86 apply zenon_H49. apply sym_equal. exact zenon_H48. % 4.69/4.86 (* end of lemma zenon_L170_ *) % 4.69/4.86 assert (zenon_L171_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> False). % 4.69/4.86 do 0 intro. intros zenon_H4b zenon_H179 zenon_Hf0 zenon_H41 zenon_H4c zenon_H4d. % 4.69/4.86 apply (zenon_or_s _ _ zenon_H4b); [ zenon_intro zenon_H43 | zenon_intro zenon_H4e ]. % 4.69/4.86 exact (zenon_H179 zenon_H43). % 4.69/4.86 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H48 | zenon_intro zenon_H4f ]. % 4.69/4.86 apply (zenon_L170_); trivial. % 4.69/4.86 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H51 | zenon_intro zenon_H50 ]. % 4.69/4.86 exact (zenon_H4c zenon_H51). % 4.69/4.86 exact (zenon_H4d zenon_H50). % 4.69/4.86 (* end of lemma zenon_L171_ *) % 4.69/4.86 assert (zenon_L172_ : ((op (e3) (e0)) = (e1)) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> False). % 4.69/4.86 do 0 intro. intros zenon_H123 zenon_H2e zenon_H13c. % 4.69/4.86 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H55 | zenon_intro zenon_H56 ]. % 4.69/4.86 cut (((e3) = (e3)) = ((e1) = (e3))). % 4.69/4.86 intro zenon_D_pnotp. % 4.69/4.86 apply zenon_H13c. % 4.69/4.86 rewrite <- zenon_D_pnotp. % 4.69/4.86 exact zenon_H55. % 4.69/4.86 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H56]. % 4.69/4.86 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H13d]. % 4.69/4.86 congruence. % 4.69/4.86 cut (((op (e3) (e0)) = (e1)) = ((e3) = (e1))). % 4.69/4.86 intro zenon_D_pnotp. % 4.69/4.86 apply zenon_H13d. % 4.69/4.86 rewrite <- zenon_D_pnotp. % 4.69/4.86 exact zenon_H123. % 4.69/4.86 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 4.69/4.86 cut (((op (e3) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 4.69/4.86 congruence. % 4.69/4.86 exact (zenon_H29 zenon_H2e). % 4.69/4.86 apply zenon_H9b. apply refl_equal. % 4.69/4.86 apply zenon_H56. apply refl_equal. % 4.69/4.86 apply zenon_H56. apply refl_equal. % 4.69/4.86 (* end of lemma zenon_L172_ *) % 4.69/4.86 assert (zenon_L173_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> False). % 4.69/4.86 do 0 intro. intros zenon_H28 zenon_H13c zenon_H123 zenon_H2a zenon_H2b zenon_H2c. % 4.69/4.86 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2e | zenon_intro zenon_H2d ]. % 4.69/4.86 apply (zenon_L172_); trivial. % 4.69/4.86 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H30 | zenon_intro zenon_H2f ]. % 4.69/4.86 exact (zenon_H2a zenon_H30). % 4.69/4.86 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 4.69/4.86 exact (zenon_H2b zenon_H32). % 4.69/4.86 exact (zenon_H2c zenon_H31). % 4.69/4.86 (* end of lemma zenon_L173_ *) % 4.69/4.86 assert (zenon_L174_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((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))))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 4.69/4.86 do 0 intro. intros zenon_H100 zenon_H2b zenon_H4d zenon_H13c zenon_H18f zenon_H38 zenon_H19d zenon_H36 zenon_Hc3 zenon_H33 zenon_H9d zenon_Hb8 zenon_H26 zenon_H82. % 4.69/4.86 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hb6 | zenon_intro zenon_H105 ]. % 4.69/4.86 apply (zenon_L147_); trivial. % 4.69/4.86 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H5e | zenon_intro zenon_H106 ]. % 4.69/4.86 apply (zenon_L164_); trivial. % 4.69/4.86 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_H92 | zenon_intro zenon_H8a ]. % 4.69/4.86 apply (zenon_L149_); trivial. % 4.69/4.86 apply (zenon_L63_); trivial. % 4.69/4.86 (* end of lemma zenon_L174_ *) % 4.69/4.86 assert (zenon_L175_ : (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e2)) -> ((op (e3) (e3)) = (e2)) -> False). % 4.69/4.86 do 0 intro. intros zenon_Hf9 zenon_Ha5 zenon_H79. % 4.69/4.86 cut (((op (e3) (e1)) = (e2)) = ((op (e3) (e1)) = (op (e3) (e3)))). % 4.69/4.86 intro zenon_D_pnotp. % 4.69/4.86 apply zenon_Hf9. % 4.69/4.86 rewrite <- zenon_D_pnotp. % 4.69/4.86 exact zenon_Ha5. % 4.69/4.86 cut (((e2) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1aa]. % 4.69/4.86 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Ha8]. % 4.69/4.86 congruence. % 4.69/4.86 apply zenon_Ha8. apply refl_equal. % 4.69/4.86 apply zenon_H1aa. apply sym_equal. exact zenon_H79. % 4.69/4.86 (* end of lemma zenon_L175_ *) % 4.69/4.86 assert (zenon_L176_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((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) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 4.69/4.86 do 0 intro. intros zenon_H103 zenon_H104 zenon_H2c zenon_Hf9 zenon_Hdc zenon_H86 zenon_H70 zenon_Ha1 zenon_Hd7 zenon_Hda zenon_H145 zenon_H75 zenon_H4d zenon_Hd0 zenon_H42 zenon_He2 zenon_H96 zenon_H35 zenon_H33 zenon_Hc3 zenon_H36 zenon_H19d zenon_H38 zenon_Hac zenon_Hfd zenon_H92 zenon_H26 zenon_H54. % 4.69/4.86 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_H108 | zenon_intro zenon_H107 ]. % 4.69/4.86 exact (zenon_H104 zenon_H108). % 4.69/4.86 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H109 ]. % 4.69/4.86 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H5e | zenon_intro zenon_Had ]. % 4.69/4.86 apply (zenon_L164_); trivial. % 4.69/4.86 apply (zenon_or_s _ _ zenon_Had); [ zenon_intro zenon_H40 | zenon_intro zenon_Hae ]. % 4.69/4.86 cut (((op (e1) (e0)) = (e2)) = ((op (e1) (e0)) = (op (e1) (e1)))). % 4.69/4.86 intro zenon_D_pnotp. % 4.69/4.86 apply zenon_H35. % 4.69/4.86 rewrite <- zenon_D_pnotp. % 4.69/4.86 exact zenon_Ha1. % 4.69/4.86 cut (((e2) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H19e]. % 4.69/4.86 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H3c]. % 4.69/4.86 congruence. % 4.69/4.86 apply zenon_H3c. apply refl_equal. % 4.69/4.86 apply zenon_H19e. apply sym_equal. exact zenon_H40. % 4.69/4.86 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 4.69/4.86 exact (zenon_H96 zenon_H9a). % 4.69/4.86 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H53 | zenon_intro zenon_He3 ]. % 4.69/4.86 apply (zenon_L8_); trivial. % 4.69/4.86 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H5d | zenon_intro zenon_He4 ]. % 4.69/4.86 apply (zenon_L39_); trivial. % 4.69/4.86 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H50 | zenon_intro zenon_H8d ]. % 4.69/4.86 exact (zenon_H4d zenon_H50). % 4.69/4.86 apply (zenon_or_s _ _ zenon_H75); [ zenon_intro zenon_H6d | zenon_intro zenon_H77 ]. % 4.69/4.86 exact (zenon_H145 zenon_H6d). % 4.69/4.86 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H72 | zenon_intro zenon_H78 ]. % 4.69/4.86 apply (zenon_L45_); trivial. % 4.69/4.86 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H79 | zenon_intro zenon_H31 ]. % 4.69/4.86 apply (zenon_L175_); trivial. % 4.69/4.86 exact (zenon_H2c zenon_H31). % 4.69/4.86 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Hed | zenon_intro zenon_H8c ]. % 4.69/4.86 apply (zenon_L62_); trivial. % 4.69/4.86 apply (zenon_L60_); trivial. % 4.69/4.86 (* end of lemma zenon_L176_ *) % 4.69/4.86 assert (zenon_L177_ : ((op (e3) (e0)) = (e2)) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> False). % 4.69/4.86 do 0 intro. intros zenon_Hb0 zenon_H2e zenon_Hfd. % 4.69/4.86 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H55 | zenon_intro zenon_H56 ]. % 4.69/4.86 cut (((e3) = (e3)) = ((e2) = (e3))). % 4.69/4.86 intro zenon_D_pnotp. % 4.69/4.86 apply zenon_Hfd. % 4.69/4.86 rewrite <- zenon_D_pnotp. % 4.69/4.86 exact zenon_H55. % 4.69/4.86 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H56]. % 4.69/4.86 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hfe]. % 4.69/4.86 congruence. % 4.69/4.86 cut (((op (e3) (e0)) = (e2)) = ((e3) = (e2))). % 4.69/4.86 intro zenon_D_pnotp. % 4.69/4.86 apply zenon_Hfe. % 4.69/4.86 rewrite <- zenon_D_pnotp. % 4.69/4.86 exact zenon_Hb0. % 4.69/4.86 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 4.69/4.86 cut (((op (e3) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 4.69/4.86 congruence. % 4.69/4.86 exact (zenon_H29 zenon_H2e). % 4.69/4.86 apply zenon_H5c. apply refl_equal. % 4.69/4.86 apply zenon_H56. apply refl_equal. % 4.69/4.86 apply zenon_H56. apply refl_equal. % 4.69/4.86 (* end of lemma zenon_L177_ *) % 4.69/4.86 assert (zenon_L178_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> False). % 4.69/4.86 do 0 intro. intros zenon_H28 zenon_Hfd zenon_Hb0 zenon_H2a zenon_H2b zenon_H2c. % 4.69/4.86 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2e | zenon_intro zenon_H2d ]. % 4.69/4.86 apply (zenon_L177_); trivial. % 4.69/4.86 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H30 | zenon_intro zenon_H2f ]. % 4.69/4.86 exact (zenon_H2a zenon_H30). % 4.69/4.86 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 4.69/4.86 exact (zenon_H2b zenon_H32). % 4.69/4.86 exact (zenon_H2c zenon_H31). % 4.69/4.86 (* end of lemma zenon_L178_ *) % 4.69/4.86 assert (zenon_L179_ : ((op (e2) (e0)) = (e0)) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> False). % 4.69/4.86 do 0 intro. intros zenon_H42 zenon_H34 zenon_H1ab. % 4.69/4.86 elim (classic ((op (e2) (e0)) = (op (e2) (e0)))); [ zenon_intro zenon_H1ac | zenon_intro zenon_H45 ]. % 4.69/4.86 cut (((op (e2) (e0)) = (op (e2) (e0))) = ((op (e1) (e0)) = (op (e2) (e0)))). % 4.69/4.86 intro zenon_D_pnotp. % 4.69/4.86 apply zenon_H1ab. % 4.69/4.86 rewrite <- zenon_D_pnotp. % 4.69/4.86 exact zenon_H1ac. % 4.69/4.86 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H45]. % 4.69/4.86 cut (((op (e2) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1ad]. % 4.69/4.86 congruence. % 4.69/4.86 cut (((op (e2) (e0)) = (e0)) = ((op (e2) (e0)) = (op (e1) (e0)))). % 4.69/4.86 intro zenon_D_pnotp. % 4.69/4.86 apply zenon_H1ad. % 4.69/4.86 rewrite <- zenon_D_pnotp. % 4.69/4.86 exact zenon_H42. % 4.69/4.86 cut (((e0) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hc1]. % 4.69/4.86 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H45]. % 4.69/4.86 congruence. % 4.69/4.86 apply zenon_H45. apply refl_equal. % 4.69/4.86 apply zenon_Hc1. apply sym_equal. exact zenon_H34. % 4.69/4.86 apply zenon_H45. apply refl_equal. % 4.69/4.86 apply zenon_H45. apply refl_equal. % 4.69/4.86 (* end of lemma zenon_L179_ *) % 4.69/4.86 assert (zenon_L180_ : (~((op (e1) (op (e1) (e1))) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e2)) -> False). % 4.69/4.86 do 0 intro. intros zenon_H1ae zenon_H40. % 4.69/4.86 cut (((op (e1) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 4.69/4.86 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 4.69/4.86 congruence. % 4.69/4.86 apply zenon_H9b. apply refl_equal. % 4.69/4.86 exact (zenon_H37 zenon_H40). % 4.69/4.86 (* end of lemma zenon_L180_ *) % 4.69/4.86 assert (zenon_L181_ : ((op (e0) (e2)) = (e3)) -> ((op (e1) (e2)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> False). % 4.69/4.86 do 0 intro. intros zenon_Hed zenon_He5 zenon_H40. % 4.69/4.86 apply (zenon_notand_s _ _ ax9); [ zenon_intro zenon_H15a | zenon_intro zenon_H1af ]. % 4.69/4.86 elim (classic ((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hc7 ]. % 4.69/4.86 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1)))) = ((e0) = (op (e1) (op (e1) (e1))))). % 4.69/4.86 intro zenon_D_pnotp. % 4.69/4.86 apply zenon_H15a. % 4.69/4.86 rewrite <- zenon_D_pnotp. % 4.69/4.86 exact zenon_Hc6. % 4.69/4.86 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_Hc7]. % 4.69/4.86 cut (((op (e1) (op (e1) (e1))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H15b]. % 4.69/4.86 congruence. % 4.69/4.86 cut (((op (e1) (e2)) = (e0)) = ((op (e1) (op (e1) (e1))) = (e0))). % 4.69/4.86 intro zenon_D_pnotp. % 4.69/4.86 apply zenon_H15b. % 4.69/4.86 rewrite <- zenon_D_pnotp. % 4.69/4.86 exact zenon_He5. % 4.69/4.86 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 4.69/4.86 cut (((op (e1) (e2)) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1b0]. % 4.69/4.86 congruence. % 4.69/4.86 elim (classic ((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hc7 ]. % 4.69/4.86 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1)))) = ((op (e1) (e2)) = (op (e1) (op (e1) (e1))))). % 4.69/4.86 intro zenon_D_pnotp. % 4.69/4.86 apply zenon_H1b0. % 4.69/4.86 rewrite <- zenon_D_pnotp. % 4.69/4.86 exact zenon_Hc6. % 4.69/4.86 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_Hc7]. % 4.69/4.86 cut (((op (e1) (op (e1) (e1))) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1ae]. % 4.69/4.86 congruence. % 4.69/4.86 apply (zenon_L180_); trivial. % 4.69/4.86 apply zenon_Hc7. apply refl_equal. % 4.69/4.86 apply zenon_Hc7. apply refl_equal. % 4.69/4.86 apply zenon_H52. apply refl_equal. % 4.69/4.86 apply zenon_Hc7. apply refl_equal. % 4.69/4.86 apply zenon_Hc7. apply refl_equal. % 4.69/4.86 apply (zenon_notand_s _ _ zenon_H1af); [ zenon_intro zenon_H19e | zenon_intro zenon_Hca ]. % 4.69/4.86 apply zenon_H19e. apply sym_equal. exact zenon_H40. % 4.69/4.86 elim (classic ((op (op (e1) (op (e1) (e1))) (op (e1) (e1))) = (op (op (e1) (op (e1) (e1))) (op (e1) (e1))))); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hcc ]. % 4.69/4.86 cut (((op (op (e1) (op (e1) (e1))) (op (e1) (e1))) = (op (op (e1) (op (e1) (e1))) (op (e1) (e1)))) = ((e3) = (op (op (e1) (op (e1) (e1))) (op (e1) (e1))))). % 4.69/4.86 intro zenon_D_pnotp. % 4.69/4.86 apply zenon_Hca. % 4.69/4.86 rewrite <- zenon_D_pnotp. % 4.69/4.86 exact zenon_Hcb. % 4.69/4.86 cut (((op (op (e1) (op (e1) (e1))) (op (e1) (e1))) = (op (op (e1) (op (e1) (e1))) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_Hcc]. % 4.69/4.86 cut (((op (op (e1) (op (e1) (e1))) (op (e1) (e1))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hcd]. % 4.69/4.86 congruence. % 4.69/4.86 cut (((op (e0) (e2)) = (e3)) = ((op (op (e1) (op (e1) (e1))) (op (e1) (e1))) = (e3))). % 4.69/4.86 intro zenon_D_pnotp. % 4.69/4.86 apply zenon_Hcd. % 4.69/4.86 rewrite <- zenon_D_pnotp. % 4.69/4.86 exact zenon_Hed. % 4.69/4.86 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H56]. % 4.69/4.86 cut (((op (e0) (e2)) = (op (op (e1) (op (e1) (e1))) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1b1]. % 4.69/4.86 congruence. % 4.69/4.86 elim (classic ((op (op (e1) (op (e1) (e1))) (op (e1) (e1))) = (op (op (e1) (op (e1) (e1))) (op (e1) (e1))))); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hcc ]. % 4.69/4.86 cut (((op (op (e1) (op (e1) (e1))) (op (e1) (e1))) = (op (op (e1) (op (e1) (e1))) (op (e1) (e1)))) = ((op (e0) (e2)) = (op (op (e1) (op (e1) (e1))) (op (e1) (e1))))). % 4.69/4.86 intro zenon_D_pnotp. % 4.69/4.86 apply zenon_H1b1. % 4.69/4.86 rewrite <- zenon_D_pnotp. % 4.69/4.86 exact zenon_Hcb. % 4.69/4.86 cut (((op (op (e1) (op (e1) (e1))) (op (e1) (e1))) = (op (op (e1) (op (e1) (e1))) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_Hcc]. % 4.69/4.86 cut (((op (op (e1) (op (e1) (e1))) (op (e1) (e1))) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1b2]. % 4.69/4.86 congruence. % 4.69/4.86 cut (((op (e1) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 4.69/4.86 cut (((op (e1) (op (e1) (e1))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H15b]. % 4.69/4.86 congruence. % 4.69/4.86 cut (((op (e1) (e2)) = (e0)) = ((op (e1) (op (e1) (e1))) = (e0))). % 4.69/4.86 intro zenon_D_pnotp. % 4.69/4.86 apply zenon_H15b. % 4.69/4.86 rewrite <- zenon_D_pnotp. % 4.69/4.86 exact zenon_He5. % 4.69/4.86 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 4.69/4.86 cut (((op (e1) (e2)) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1b0]. % 4.69/4.86 congruence. % 4.69/4.86 elim (classic ((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hc7 ]. % 4.69/4.86 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1)))) = ((op (e1) (e2)) = (op (e1) (op (e1) (e1))))). % 4.69/4.86 intro zenon_D_pnotp. % 4.69/4.86 apply zenon_H1b0. % 4.69/4.86 rewrite <- zenon_D_pnotp. % 4.69/4.86 exact zenon_Hc6. % 4.69/4.86 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_Hc7]. % 4.69/4.86 cut (((op (e1) (op (e1) (e1))) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1ae]. % 4.69/4.86 congruence. % 4.69/4.86 apply (zenon_L180_); trivial. % 4.69/4.86 apply zenon_Hc7. apply refl_equal. % 4.69/4.86 apply zenon_Hc7. apply refl_equal. % 4.69/4.86 apply zenon_H52. apply refl_equal. % 4.69/4.86 exact (zenon_H37 zenon_H40). % 4.69/4.86 apply zenon_Hcc. apply refl_equal. % 4.69/4.86 apply zenon_Hcc. apply refl_equal. % 4.69/4.86 apply zenon_H56. apply refl_equal. % 4.69/4.86 apply zenon_Hcc. apply refl_equal. % 4.69/4.86 apply zenon_Hcc. apply refl_equal. % 4.69/4.86 (* end of lemma zenon_L181_ *) % 4.69/4.86 assert (zenon_L182_ : ((op (e1) (e2)) = (e0)) -> ((op (e1) (e2)) = (e2)) -> (~((e0) = (e2))) -> False). % 4.69/4.86 do 0 intro. intros zenon_He5 zenon_Ha2 zenon_H82. % 4.69/4.86 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H83 | zenon_intro zenon_H5c ]. % 4.69/4.86 cut (((e2) = (e2)) = ((e0) = (e2))). % 4.69/4.86 intro zenon_D_pnotp. % 4.69/4.86 apply zenon_H82. % 4.69/4.86 rewrite <- zenon_D_pnotp. % 4.69/4.86 exact zenon_H83. % 4.69/4.86 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 4.69/4.86 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 4.69/4.86 congruence. % 4.69/4.86 cut (((op (e1) (e2)) = (e0)) = ((e2) = (e0))). % 4.69/4.86 intro zenon_D_pnotp. % 4.69/4.86 apply zenon_H84. % 4.69/4.86 rewrite <- zenon_D_pnotp. % 4.69/4.86 exact zenon_He5. % 4.69/4.86 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 4.69/4.86 cut (((op (e1) (e2)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1b3]. % 4.69/4.86 congruence. % 4.69/4.86 exact (zenon_H1b3 zenon_Ha2). % 4.69/4.86 apply zenon_H52. apply refl_equal. % 4.69/4.86 apply zenon_H5c. apply refl_equal. % 4.69/4.86 apply zenon_H5c. apply refl_equal. % 4.69/4.86 (* end of lemma zenon_L182_ *) % 4.69/4.86 assert (zenon_L183_ : ((op (e1) (e3)) = (e2)) -> ((op (e1) (e3)) = (e3)) -> (~((e2) = (e3))) -> False). % 4.69/4.86 do 0 intro. intros zenon_Hd8 zenon_Hdb zenon_Hfd. % 4.69/4.86 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H55 | zenon_intro zenon_H56 ]. % 4.69/4.86 cut (((e3) = (e3)) = ((e2) = (e3))). % 4.69/4.86 intro zenon_D_pnotp. % 4.69/4.86 apply zenon_Hfd. % 4.69/4.86 rewrite <- zenon_D_pnotp. % 4.69/4.86 exact zenon_H55. % 4.69/4.86 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H56]. % 4.69/4.86 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hfe]. % 4.69/4.86 congruence. % 4.69/4.86 cut (((op (e1) (e3)) = (e2)) = ((e3) = (e2))). % 4.69/4.86 intro zenon_D_pnotp. % 4.69/4.86 apply zenon_Hfe. % 4.69/4.86 rewrite <- zenon_D_pnotp. % 4.69/4.86 exact zenon_Hd8. % 4.69/4.86 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 4.69/4.86 cut (((op (e1) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H164]. % 4.69/4.86 congruence. % 4.69/4.86 exact (zenon_H164 zenon_Hdb). % 4.69/4.86 apply zenon_H5c. apply refl_equal. % 4.69/4.86 apply zenon_H56. apply refl_equal. % 4.69/4.86 apply zenon_H56. apply refl_equal. % 4.69/4.86 (* end of lemma zenon_L183_ *) % 4.69/4.86 assert (zenon_L184_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e2)) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> False). % 4.69/4.86 do 0 intro. intros zenon_H165 zenon_H9d zenon_H82 zenon_He5 zenon_H166 zenon_H13c zenon_H7e zenon_H38 zenon_Hed zenon_H132 zenon_Hfd. % 4.69/4.86 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_Ha1 | zenon_intro zenon_H167 ]. % 4.69/4.86 apply (zenon_L118_); trivial. % 4.69/4.86 apply (zenon_or_s _ _ zenon_H167); [ zenon_intro zenon_H40 | zenon_intro zenon_H168 ]. % 4.69/4.86 apply (zenon_L181_); trivial. % 4.69/4.86 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hd8 ]. % 4.69/4.86 apply (zenon_L182_); trivial. % 4.69/4.86 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H156 | zenon_intro zenon_H169 ]. % 4.69/4.86 apply (zenon_L119_); trivial. % 4.69/4.86 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H3f | zenon_intro zenon_H16a ]. % 4.69/4.86 exact (zenon_H38 zenon_H3f). % 4.69/4.86 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H162 | zenon_intro zenon_Hdb ]. % 4.69/4.86 cut (((op (e0) (e2)) = (e3)) = ((op (e0) (e2)) = (op (e1) (e2)))). % 4.69/4.86 intro zenon_D_pnotp. % 4.69/4.86 apply zenon_H132. % 4.69/4.86 rewrite <- zenon_D_pnotp. % 4.69/4.86 exact zenon_Hed. % 4.69/4.86 cut (((e3) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1b4]. % 4.69/4.86 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H134]. % 4.69/4.86 congruence. % 4.69/4.86 apply zenon_H134. apply refl_equal. % 4.69/4.86 apply zenon_H1b4. apply sym_equal. exact zenon_H162. % 4.69/4.86 apply (zenon_L183_); trivial. % 4.69/4.86 (* end of lemma zenon_L184_ *) % 4.69/4.86 assert (zenon_L185_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e3)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e2)) -> False). % 4.69/4.86 do 0 intro. intros zenon_Ha9 zenon_Hfd zenon_Hed zenon_Ha1 zenon_Ha0 zenon_H4c zenon_Ha4 zenon_Ha5. % 4.69/4.86 apply (zenon_or_s _ _ zenon_Ha9); [ zenon_intro zenon_H92 | zenon_intro zenon_Haa ]. % 4.69/4.86 apply (zenon_L62_); trivial. % 4.69/4.86 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hab ]. % 4.69/4.86 apply (zenon_L27_); trivial. % 4.69/4.86 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H51 | zenon_intro zenon_Ha6 ]. % 4.69/4.86 exact (zenon_H4c zenon_H51). % 4.69/4.86 apply (zenon_L28_); trivial. % 4.69/4.86 (* end of lemma zenon_L185_ *) % 4.69/4.86 assert (zenon_L186_ : ((op (e1) (e3)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> (~((e1) = (e2))) -> False). % 4.69/4.86 do 0 intro. intros zenon_H71 zenon_Hd8 zenon_H9d. % 4.69/4.86 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H83 | zenon_intro zenon_H5c ]. % 4.69/4.86 cut (((e2) = (e2)) = ((e1) = (e2))). % 4.69/4.86 intro zenon_D_pnotp. % 4.69/4.86 apply zenon_H9d. % 4.69/4.86 rewrite <- zenon_D_pnotp. % 4.69/4.86 exact zenon_H83. % 4.69/4.86 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 4.69/4.86 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9e]. % 4.69/4.86 congruence. % 4.69/4.86 cut (((op (e1) (e3)) = (e1)) = ((e2) = (e1))). % 4.69/4.86 intro zenon_D_pnotp. % 4.69/4.86 apply zenon_H9e. % 4.69/4.86 rewrite <- zenon_D_pnotp. % 4.69/4.86 exact zenon_H71. % 4.69/4.86 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 4.69/4.86 cut (((op (e1) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1b5]. % 4.69/4.86 congruence. % 4.69/4.86 exact (zenon_H1b5 zenon_Hd8). % 4.69/4.86 apply zenon_H9b. apply refl_equal. % 4.69/4.86 apply zenon_H5c. apply refl_equal. % 4.69/4.86 apply zenon_H5c. apply refl_equal. % 4.69/4.86 (* end of lemma zenon_L186_ *) % 4.69/4.86 assert (zenon_L187_ : ((op (e3) (e0)) = (e0)) -> ((op (e3) (e0)) = (e3)) -> (~((e0) = (e3))) -> False). % 4.69/4.86 do 0 intro. intros zenon_Hbd zenon_H2e zenon_H54. % 4.69/4.86 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H55 | zenon_intro zenon_H56 ]. % 4.69/4.86 cut (((e3) = (e3)) = ((e0) = (e3))). % 4.69/4.86 intro zenon_D_pnotp. % 4.69/4.86 apply zenon_H54. % 4.69/4.86 rewrite <- zenon_D_pnotp. % 4.69/4.86 exact zenon_H55. % 4.69/4.86 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H56]. % 4.69/4.86 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 4.69/4.86 congruence. % 4.69/4.86 cut (((op (e3) (e0)) = (e0)) = ((e3) = (e0))). % 4.69/4.86 intro zenon_D_pnotp. % 4.69/4.86 apply zenon_H57. % 4.69/4.86 rewrite <- zenon_D_pnotp. % 4.69/4.86 exact zenon_Hbd. % 4.69/4.86 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 4.69/4.86 cut (((op (e3) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 4.69/4.86 congruence. % 4.69/4.86 exact (zenon_H29 zenon_H2e). % 4.69/4.86 apply zenon_H52. apply refl_equal. % 4.69/4.86 apply zenon_H56. apply refl_equal. % 4.69/4.86 apply zenon_H56. apply refl_equal. % 4.69/4.86 (* end of lemma zenon_L187_ *) % 4.69/4.86 assert (zenon_L188_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> False). % 4.69/4.86 do 0 intro. intros zenon_H28 zenon_H54 zenon_Hbd zenon_H2a zenon_H2b zenon_H2c. % 4.69/4.86 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2e | zenon_intro zenon_H2d ]. % 4.69/4.86 apply (zenon_L187_); trivial. % 4.69/4.86 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H30 | zenon_intro zenon_H2f ]. % 4.69/4.86 exact (zenon_H2a zenon_H30). % 4.69/4.86 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 4.69/4.86 exact (zenon_H2b zenon_H32). % 4.69/4.86 exact (zenon_H2c zenon_H31). % 4.69/4.86 (* end of lemma zenon_L188_ *) % 4.69/4.86 assert (zenon_L189_ : (((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 (e1) (e1)) = (e3))) -> False). % 4.69/4.86 do 0 intro. intros zenon_H33 zenon_Hc3 zenon_H36 zenon_H37 zenon_H38. % 4.69/4.86 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H3a | zenon_intro zenon_H39 ]. % 4.69/4.86 exact (zenon_Hc3 zenon_H3a). % 4.69/4.86 apply (zenon_or_s _ _ zenon_H39); [ zenon_intro zenon_H3e | zenon_intro zenon_H3d ]. % 4.69/4.86 exact (zenon_H36 zenon_H3e). % 4.69/4.86 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H40 | zenon_intro zenon_H3f ]. % 4.69/4.86 exact (zenon_H37 zenon_H40). % 4.69/4.86 exact (zenon_H38 zenon_H3f). % 4.69/4.86 (* end of lemma zenon_L189_ *) % 4.69/4.86 assert (zenon_L190_ : (((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) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (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 (e0) (e2)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 4.69/4.86 do 0 intro. intros zenon_H103 zenon_H104 zenon_H9c zenon_H86 zenon_H165 zenon_H9d zenon_H82 zenon_H166 zenon_H13c zenon_H7e zenon_H38 zenon_H132 zenon_Hfd zenon_Hc3 zenon_H42 zenon_H1ab zenon_He9 zenon_H26 zenon_H54. % 4.69/4.86 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_H108 | zenon_intro zenon_H107 ]. % 4.69/4.86 exact (zenon_H104 zenon_H108). % 4.69/4.86 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H109 ]. % 4.69/4.86 apply (zenon_L114_); trivial. % 4.69/4.86 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Hed | zenon_intro zenon_H8c ]. % 4.69/4.86 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H34 | zenon_intro zenon_Hea ]. % 4.69/4.86 apply (zenon_L179_); trivial. % 4.69/4.86 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H3a | zenon_intro zenon_Heb ]. % 4.69/4.86 exact (zenon_Hc3 zenon_H3a). % 4.69/4.86 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_He5 | zenon_intro zenon_H7a ]. % 4.69/4.86 apply (zenon_L184_); trivial. % 4.69/4.86 apply (zenon_L42_); trivial. % 4.69/4.86 apply (zenon_L60_); trivial. % 4.69/4.86 (* end of lemma zenon_L190_ *) % 4.69/4.86 assert (zenon_L191_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> False). % 4.69/4.86 do 0 intro. intros zenon_H11f zenon_H1e zenon_H5b zenon_H2b zenon_H4d zenon_Hb8 zenon_H13c zenon_H18f zenon_H104. % 4.69/4.86 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H23 | zenon_intro zenon_H120 ]. % 4.69/4.86 exact (zenon_H1e zenon_H23). % 4.69/4.86 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H5a | zenon_intro zenon_H121 ]. % 4.69/4.86 exact (zenon_H5b zenon_H5a). % 4.69/4.86 apply (zenon_or_s _ _ zenon_H121); [ zenon_intro zenon_Hb6 | zenon_intro zenon_H108 ]. % 4.69/4.86 apply (zenon_L147_); trivial. % 4.69/4.86 exact (zenon_H104 zenon_H108). % 4.69/4.86 (* end of lemma zenon_L191_ *) % 4.69/4.86 assert (zenon_L192_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (((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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 4.69/4.86 do 0 intro. intros zenon_H118 zenon_H2c zenon_H2a zenon_H28 zenon_H42 zenon_H103 zenon_H86 zenon_H165 zenon_H9d zenon_H82 zenon_H166 zenon_H38 zenon_H132 zenon_Hfd zenon_Hc3 zenon_H1ab zenon_He9 zenon_H54 zenon_H137 zenon_H104 zenon_H18f zenon_H13c zenon_H4d zenon_H2b zenon_H5b zenon_H1e zenon_H11f zenon_H26 zenon_Hb9. % 4.69/4.86 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H5a | zenon_intro zenon_H119 ]. % 4.69/4.86 exact (zenon_H5b zenon_H5a). % 4.69/4.86 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H9c | zenon_intro zenon_H11c ]. % 4.69/4.86 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_H5a | zenon_intro zenon_H138 ]. % 4.69/4.86 exact (zenon_H5b zenon_H5a). % 4.69/4.86 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_H7e | zenon_intro zenon_H139 ]. % 4.69/4.86 apply (zenon_L190_); trivial. % 4.69/4.86 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H123 ]. % 4.69/4.86 apply (zenon_L100_); trivial. % 4.69/4.86 apply (zenon_L173_); trivial. % 4.69/4.86 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H87 ]. % 4.69/4.86 apply (zenon_L191_); trivial. % 4.69/4.86 apply (zenon_L40_); trivial. % 4.69/4.86 (* end of lemma zenon_L192_ *) % 4.69/4.86 assert (zenon_L193_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> False). % 4.69/4.86 do 0 intro. intros zenon_H4b zenon_H179 zenon_H16c zenon_H4c zenon_H4d. % 4.69/4.86 apply (zenon_or_s _ _ zenon_H4b); [ zenon_intro zenon_H43 | zenon_intro zenon_H4e ]. % 4.69/4.86 exact (zenon_H179 zenon_H43). % 4.69/4.86 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H48 | zenon_intro zenon_H4f ]. % 4.69/4.86 exact (zenon_H16c zenon_H48). % 4.69/4.86 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H51 | zenon_intro zenon_H50 ]. % 4.69/4.86 exact (zenon_H4c zenon_H51). % 4.69/4.86 exact (zenon_H4d zenon_H50). % 4.69/4.86 (* end of lemma zenon_L193_ *) % 4.69/4.86 assert (zenon_L194_ : ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e0)) = (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))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> False). % 4.69/4.86 do 0 intro. intros zenon_H19b zenon_H1d zenon_H137 zenon_H13c zenon_H2c zenon_H28 zenon_H179 zenon_H41 zenon_H4c zenon_H4d zenon_H4b zenon_Hb9 zenon_H5b zenon_H118 zenon_H18f zenon_H11f zenon_H103 zenon_H54 zenon_H1ab zenon_Hc3 zenon_H165 zenon_H38 zenon_H132 zenon_Hfd zenon_H166 zenon_H82 zenon_H9d zenon_H86 zenon_He9 zenon_H104 zenon_H114 zenon_H20 zenon_H1f zenon_H1e zenon_H19a. % 4.69/4.86 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H2a | zenon_intro zenon_H16c ]. % 4.69/4.86 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H2b | zenon_intro zenon_Hb4 ]. % 4.69/4.86 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ]. % 4.69/4.86 exact (zenon_H1e zenon_H23). % 4.69/4.86 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ]. % 4.69/4.86 exact (zenon_H1f zenon_H25). % 4.69/4.86 apply (zenon_or_s _ _ zenon_H24); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 4.69/4.86 exact (zenon_H20 zenon_H27). % 4.69/4.86 apply (zenon_or_s _ _ zenon_H114); [ zenon_intro zenon_H23 | zenon_intro zenon_H115 ]. % 4.69/4.86 exact (zenon_H1e zenon_H23). % 4.69/4.86 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H34 | zenon_intro zenon_H116 ]. % 4.69/4.86 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_H5a | zenon_intro zenon_H138 ]. % 4.69/4.86 exact (zenon_H5b zenon_H5a). % 4.69/4.86 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_H7e | zenon_intro zenon_H139 ]. % 4.69/4.86 apply (zenon_L110_); trivial. % 4.69/4.86 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H123 ]. % 4.69/4.86 apply (zenon_L171_); trivial. % 4.69/4.86 apply (zenon_L173_); trivial. % 4.69/4.86 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H42 | zenon_intro zenon_Hbd ]. % 4.69/4.86 apply (zenon_L192_); trivial. % 4.69/4.86 apply (zenon_L188_); trivial. % 4.69/4.86 apply (zenon_L73_); trivial. % 4.69/4.86 apply (zenon_L193_); trivial. % 4.69/4.86 (* end of lemma zenon_L194_ *) % 4.69/4.86 assert (zenon_L195_ : ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (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)))) -> (((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 (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> False). % 4.69/4.86 do 0 intro. intros zenon_H1b6 zenon_H122 zenon_H177 zenon_H171 zenon_H154 zenon_H153 zenon_H113 zenon_H75 zenon_H70 zenon_H142 zenon_H117 zenon_H13e zenon_Hdf zenon_H12e zenon_Hb3 zenon_Haf zenon_Ha9 zenon_Ha4 zenon_Ha0 zenon_Hac zenon_H94 zenon_Hd0 zenon_H100 zenon_H36 zenon_H7b zenon_H152 zenon_H170 zenon_Hbe zenon_H16b zenon_H16f zenon_H172 zenon_H173 zenon_H174 zenon_H176 zenon_H175 zenon_H19a zenon_H1e zenon_H1f zenon_H20 zenon_H114 zenon_H104 zenon_He9 zenon_H86 zenon_H9d zenon_H82 zenon_H166 zenon_Hfd zenon_H132 zenon_H38 zenon_H165 zenon_Hc3 zenon_H1ab zenon_H54 zenon_H103 zenon_H11f zenon_H18f zenon_H118 zenon_H5b zenon_Hb9 zenon_H4b zenon_H4d zenon_H41 zenon_H179 zenon_H28 zenon_H2c zenon_H13c zenon_H137 zenon_H1d zenon_H19b. % 4.69/4.86 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H4c | zenon_intro zenon_Hb4 ]. % 4.69/4.86 apply (zenon_L194_); trivial. % 4.69/4.86 apply (zenon_L138_); trivial. % 4.69/4.86 (* end of lemma zenon_L195_ *) % 4.69/4.86 assert (zenon_L196_ : ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (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 (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> False). % 4.69/4.86 do 0 intro. intros zenon_H1b7 zenon_H19b zenon_H1d zenon_H137 zenon_H13c zenon_H2c zenon_H28 zenon_H179 zenon_H41 zenon_H4d zenon_H4b zenon_Hb9 zenon_H5b zenon_H118 zenon_H18f zenon_H11f zenon_H103 zenon_H54 zenon_H1ab zenon_Hc3 zenon_H165 zenon_H38 zenon_H132 zenon_Hfd zenon_H166 zenon_H82 zenon_H9d zenon_H86 zenon_He9 zenon_H104 zenon_H114 zenon_H20 zenon_H1f zenon_H1e zenon_H19a zenon_H175 zenon_H176 zenon_H174 zenon_H173 zenon_H172 zenon_H16f zenon_H16b zenon_Hbe zenon_H170 zenon_H152 zenon_H7b zenon_H100 zenon_Hd0 zenon_H94 zenon_Hac zenon_Ha0 zenon_Ha4 zenon_Ha9 zenon_Haf zenon_Hb3 zenon_H12e zenon_Hdf zenon_H13e zenon_H117 zenon_H142 zenon_H70 zenon_H75 zenon_H113 zenon_H153 zenon_H154 zenon_H171 zenon_H177 zenon_H122 zenon_H1b6. % 4.69/4.86 apply (zenon_or_s _ _ zenon_H1b7); [ zenon_intro zenon_H36 | zenon_intro zenon_H36 ]. % 4.69/4.86 apply (zenon_L195_); trivial. % 4.69/4.86 apply (zenon_L195_); trivial. % 4.69/4.86 (* end of lemma zenon_L196_ *) % 4.69/4.86 assert (zenon_L197_ : ((~((op (e1) (e1)) = (e1)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (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)))) -> (((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 (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> False). % 4.69/4.86 do 0 intro. intros zenon_H1b8 zenon_H1b6 zenon_H122 zenon_H177 zenon_H171 zenon_H154 zenon_H153 zenon_H113 zenon_H75 zenon_H70 zenon_H142 zenon_H117 zenon_H13e zenon_Hdf zenon_H12e zenon_Hb3 zenon_Haf zenon_Ha9 zenon_Ha4 zenon_Ha0 zenon_Hac zenon_H94 zenon_Hd0 zenon_H100 zenon_H7b zenon_H152 zenon_H170 zenon_Hbe zenon_H16b zenon_H16f zenon_H172 zenon_H173 zenon_H174 zenon_H176 zenon_H175 zenon_H19a zenon_H1e zenon_H1f zenon_H20 zenon_H114 zenon_H104 zenon_He9 zenon_H86 zenon_H9d zenon_H82 zenon_H166 zenon_Hfd zenon_H132 zenon_H165 zenon_H1ab zenon_H54 zenon_H103 zenon_H11f zenon_H18f zenon_H118 zenon_Hb9 zenon_H4b zenon_H4d zenon_H41 zenon_H179 zenon_H28 zenon_H2c zenon_H13c zenon_H137 zenon_H1d zenon_H19b zenon_H1b7 zenon_Hc3 zenon_H37 zenon_H38 zenon_H33. % 4.69/4.86 apply (zenon_or_s _ _ zenon_H1b8); [ zenon_intro zenon_H36 | zenon_intro zenon_H5b ]. % 4.69/4.86 apply (zenon_L189_); trivial. % 4.69/4.86 apply (zenon_L196_); trivial. % 4.69/4.86 (* end of lemma zenon_L197_ *) % 4.69/4.86 assert (zenon_L198_ : ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e0) (e0)) = (e1)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e2))) -> (((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))))) -> False). % 4.69/4.87 do 0 intro. intros zenon_H11e zenon_H1b7 zenon_H19b zenon_H137 zenon_H13c zenon_H41 zenon_Hb9 zenon_H118 zenon_H18f zenon_H11f zenon_H1ab zenon_H165 zenon_H132 zenon_H166 zenon_H9d zenon_He9 zenon_H19a zenon_H175 zenon_H176 zenon_H174 zenon_H173 zenon_H172 zenon_H16f zenon_H16b zenon_Hbe zenon_H170 zenon_H152 zenon_H7b zenon_H94 zenon_Ha9 zenon_Haf zenon_H12e zenon_Hdf zenon_H13e zenon_H117 zenon_H142 zenon_H113 zenon_H153 zenon_H154 zenon_H171 zenon_H177 zenon_H122 zenon_H1b6 zenon_H1b8 zenon_H1e zenon_H1f zenon_H20 zenon_H114 zenon_Hb3 zenon_H2a zenon_H28 zenon_Hac zenon_Hd0 zenon_H75 zenon_H2c zenon_Hf9 zenon_H86 zenon_H70 zenon_Hd7 zenon_Hda zenon_Hdc zenon_H145 zenon_He2 zenon_H96 zenon_H35 zenon_Hb4 zenon_H33 zenon_H38 zenon_H19d zenon_H36 zenon_Hc3 zenon_H103 zenon_H54 zenon_Hfd zenon_H4b zenon_H4d zenon_H4c zenon_H179 zenon_H102 zenon_Ha4 zenon_Ha0 zenon_H1a7 zenon_H104 zenon_H82 zenon_H100 zenon_H1d. % 4.69/4.87 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H2b | zenon_intro zenon_H37 ]. % 4.69/4.87 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ]. % 4.69/4.87 exact (zenon_H1e zenon_H23). % 4.69/4.87 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ]. % 4.69/4.87 exact (zenon_H1f zenon_H25). % 4.69/4.87 apply (zenon_or_s _ _ zenon_H24); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 4.69/4.87 exact (zenon_H20 zenon_H27). % 4.69/4.87 apply (zenon_or_s _ _ zenon_H114); [ zenon_intro zenon_H23 | zenon_intro zenon_H115 ]. % 4.69/4.87 exact (zenon_H1e zenon_H23). % 4.69/4.87 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H34 | zenon_intro zenon_H116 ]. % 4.69/4.87 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hb6 | zenon_intro zenon_H105 ]. % 4.69/4.87 exact (zenon_Hb4 zenon_Hb6). % 4.69/4.87 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H5e | zenon_intro zenon_H106 ]. % 4.69/4.87 apply (zenon_L164_); trivial. % 4.69/4.87 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_H92 | zenon_intro zenon_H8a ]. % 4.69/4.87 apply (zenon_L168_); trivial. % 4.69/4.87 apply (zenon_L63_); trivial. % 4.69/4.87 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H42 | zenon_intro zenon_Hbd ]. % 4.69/4.87 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hb6 | zenon_intro zenon_H105 ]. % 4.69/4.87 exact (zenon_Hb4 zenon_Hb6). % 4.69/4.87 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H5e | zenon_intro zenon_H106 ]. % 4.69/4.87 apply (zenon_L164_); trivial. % 4.69/4.87 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_H92 | zenon_intro zenon_H8a ]. % 4.69/4.87 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hb5 ]. % 4.69/4.87 exact (zenon_Hb4 zenon_Hb6). % 4.69/4.87 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hb7 ]. % 4.69/4.87 apply (zenon_L176_); trivial. % 4.69/4.87 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H98 | zenon_intro zenon_Hb0 ]. % 4.69/4.87 apply (zenon_L31_); trivial. % 4.69/4.87 apply (zenon_L178_); trivial. % 4.69/4.87 apply (zenon_L63_); trivial. % 4.69/4.87 apply (zenon_L188_); trivial. % 4.69/4.87 apply (zenon_L197_); trivial. % 4.69/4.87 (* end of lemma zenon_L198_ *) % 4.69/4.87 assert (zenon_L199_ : ((~((op (e3) (e1)) = (e3)))\/(~((op (e0) (e0)) = (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((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 (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e0) (e0)) = (e1)))) -> False). % 4.69/4.87 do 0 intro. intros zenon_H19c zenon_H1d zenon_H118 zenon_H18f zenon_H13c zenon_Hb9 zenon_H41 zenon_H28 zenon_H2c zenon_H137 zenon_H9d zenon_H33 zenon_H38 zenon_H19d zenon_H36 zenon_Hc3 zenon_H103 zenon_H54 zenon_Hfd zenon_H4b zenon_H4d zenon_H4c zenon_H179 zenon_H102 zenon_Ha4 zenon_Ha0 zenon_H1a7 zenon_H104 zenon_H82 zenon_H100 zenon_He9 zenon_H165 zenon_H132 zenon_H166 zenon_H195 zenon_Ha9 zenon_H7b zenon_H1ab zenon_Hb3 zenon_Hac zenon_Hd0 zenon_H75 zenon_Hf9 zenon_H86 zenon_H70 zenon_Hd7 zenon_Hda zenon_Hdc zenon_H145 zenon_He2 zenon_H96 zenon_H35 zenon_H114 zenon_H20 zenon_H1f zenon_H1e zenon_H11e zenon_H1b7 zenon_H19b zenon_H11f zenon_H19a zenon_H175 zenon_H176 zenon_H174 zenon_H173 zenon_H172 zenon_H16f zenon_H16b zenon_Hbe zenon_H170 zenon_H152 zenon_H94 zenon_Haf zenon_H12e zenon_Hdf zenon_H13e zenon_H117 zenon_H142 zenon_H113 zenon_H153 zenon_H154 zenon_H171 zenon_H177 zenon_H122 zenon_H1b6 zenon_H1b8. % 4.69/4.87 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H2a | zenon_intro zenon_H5b ]. % 4.69/4.87 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H2b | zenon_intro zenon_Hb4 ]. % 4.69/4.87 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ]. % 4.69/4.87 exact (zenon_H1e zenon_H23). % 4.69/4.87 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ]. % 4.69/4.87 exact (zenon_H1f zenon_H25). % 4.69/4.87 apply (zenon_or_s _ _ zenon_H24); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 4.69/4.87 exact (zenon_H20 zenon_H27). % 4.69/4.87 apply (zenon_or_s _ _ zenon_H114); [ zenon_intro zenon_H23 | zenon_intro zenon_H115 ]. % 4.69/4.87 exact (zenon_H1e zenon_H23). % 4.69/4.87 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H34 | zenon_intro zenon_H116 ]. % 4.69/4.87 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H5a | zenon_intro zenon_H119 ]. % 4.69/4.87 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hb6 | zenon_intro zenon_H105 ]. % 4.69/4.87 apply (zenon_L163_); trivial. % 4.69/4.87 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H5e | zenon_intro zenon_H106 ]. % 4.69/4.87 apply (zenon_L164_); trivial. % 4.69/4.87 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_H92 | zenon_intro zenon_H8a ]. % 4.69/4.87 apply (zenon_L168_); trivial. % 4.69/4.87 apply (zenon_L63_); trivial. % 4.69/4.87 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H9c | zenon_intro zenon_H11c ]. % 4.69/4.87 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_H5a | zenon_intro zenon_H138 ]. % 4.69/4.87 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hb6 | zenon_intro zenon_H105 ]. % 4.69/4.87 apply (zenon_L163_); trivial. % 4.69/4.87 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H5e | zenon_intro zenon_H106 ]. % 4.69/4.87 apply (zenon_L26_); trivial. % 4.69/4.87 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_H92 | zenon_intro zenon_H8a ]. % 4.69/4.87 apply (zenon_L169_); trivial. % 4.69/4.87 apply (zenon_L63_); trivial. % 4.69/4.87 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_H7e | zenon_intro zenon_H139 ]. % 4.69/4.87 apply (zenon_L110_); trivial. % 4.69/4.87 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H123 ]. % 4.69/4.87 apply (zenon_L171_); trivial. % 4.69/4.87 apply (zenon_L173_); trivial. % 4.69/4.87 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H87 ]. % 4.69/4.87 apply (zenon_L174_); trivial. % 4.69/4.87 apply (zenon_L40_); trivial. % 4.69/4.87 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H42 | zenon_intro zenon_Hbd ]. % 4.69/4.87 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H5a | zenon_intro zenon_H119 ]. % 4.69/4.87 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hb6 | zenon_intro zenon_H105 ]. % 4.69/4.87 apply (zenon_L163_); trivial. % 4.69/4.87 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H5e | zenon_intro zenon_H106 ]. % 4.69/4.87 apply (zenon_L164_); trivial. % 4.69/4.87 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_H92 | zenon_intro zenon_H8a ]. % 4.69/4.87 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hb5 ]. % 4.69/4.87 apply (zenon_L163_); trivial. % 4.69/4.87 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hb7 ]. % 4.69/4.87 apply (zenon_L176_); trivial. % 4.69/4.87 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H98 | zenon_intro zenon_Hb0 ]. % 4.69/4.87 apply (zenon_L31_); trivial. % 4.69/4.87 apply (zenon_L178_); trivial. % 4.69/4.87 apply (zenon_L63_); trivial. % 4.69/4.87 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H9c | zenon_intro zenon_H11c ]. % 4.69/4.87 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_H108 | zenon_intro zenon_H107 ]. % 4.69/4.87 exact (zenon_H104 zenon_H108). % 4.69/4.87 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H109 ]. % 4.69/4.87 apply (zenon_L114_); trivial. % 4.69/4.87 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Hed | zenon_intro zenon_H8c ]. % 4.69/4.87 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H34 | zenon_intro zenon_Hea ]. % 4.69/4.87 apply (zenon_L179_); trivial. % 4.69/4.87 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H3a | zenon_intro zenon_Heb ]. % 4.69/4.87 exact (zenon_Hc3 zenon_H3a). % 4.69/4.87 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_He5 | zenon_intro zenon_H7a ]. % 4.69/4.87 apply (zenon_or_s _ _ zenon_H7b); [ zenon_intro zenon_H7e | zenon_intro zenon_H7d ]. % 4.69/4.87 apply (zenon_L184_); trivial. % 4.69/4.87 apply (zenon_or_s _ _ zenon_H7d); [ zenon_intro zenon_H3e | zenon_intro zenon_H7f ]. % 4.69/4.87 exact (zenon_H36 zenon_H3e). % 4.69/4.87 apply (zenon_or_s _ _ zenon_H7f); [ zenon_intro zenon_H47 | zenon_intro zenon_H71 ]. % 4.69/4.87 exact (zenon_H195 zenon_H47). % 4.69/4.87 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_Ha1 | zenon_intro zenon_H167 ]. % 4.69/4.87 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H5e | zenon_intro zenon_Had ]. % 4.69/4.87 apply (zenon_L26_); trivial. % 4.69/4.87 apply (zenon_or_s _ _ zenon_Had); [ zenon_intro zenon_H40 | zenon_intro zenon_Hae ]. % 4.69/4.87 apply (zenon_L181_); trivial. % 4.69/4.87 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 4.69/4.87 exact (zenon_H96 zenon_H9a). % 4.69/4.87 apply (zenon_L185_); trivial. % 4.69/4.87 apply (zenon_or_s _ _ zenon_H167); [ zenon_intro zenon_H40 | zenon_intro zenon_H168 ]. % 4.69/4.87 apply (zenon_L181_); trivial. % 4.69/4.87 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hd8 ]. % 4.69/4.87 apply (zenon_L182_); trivial. % 4.69/4.87 apply (zenon_L186_); trivial. % 4.69/4.87 apply (zenon_L42_); trivial. % 4.69/4.87 apply (zenon_L60_); trivial. % 4.69/4.87 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H87 ]. % 4.69/4.87 apply (zenon_L174_); trivial. % 4.69/4.87 apply (zenon_L40_); trivial. % 4.69/4.87 apply (zenon_L188_); trivial. % 4.69/4.87 apply (zenon_L198_); trivial. % 4.69/4.87 apply (zenon_L194_); trivial. % 4.69/4.87 (* end of lemma zenon_L199_ *) % 4.69/4.87 assert (zenon_L200_ : ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (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 (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e0) (e0)) = (e1)))) -> False). % 4.69/4.87 do 0 intro. intros zenon_H1b9 zenon_H1b8 zenon_H1b6 zenon_H1b7 zenon_H1ab zenon_H1a7 zenon_H179 zenon_Hc3 zenon_H19d zenon_H19a zenon_H11d zenon_H1e zenon_H1f zenon_H114 zenon_H113 zenon_H110 zenon_H104 zenon_He9 zenon_He6 zenon_Hdc zenon_Hda zenon_Hd7 zenon_Hdf zenon_Hd0 zenon_Hbe zenon_H102 zenon_Hf6 zenon_Hef zenon_Hf3 zenon_Hf9 zenon_H101 zenon_H103 zenon_Hfd zenon_H100 zenon_H7c zenon_H4b zenon_H4d zenon_H4c zenon_H46 zenon_H41 zenon_H94 zenon_H54 zenon_H117 zenon_H86 zenon_H89 zenon_H8f zenon_H82 zenon_H7b zenon_H6c zenon_H70 zenon_H75 zenon_He2 zenon_H96 zenon_H95 zenon_Hb3 zenon_Haf zenon_H9d zenon_Ha9 zenon_Ha4 zenon_Ha0 zenon_Hac zenon_Hb9 zenon_H118 zenon_H35 zenon_H36 zenon_H38 zenon_H33 zenon_H1d zenon_H11e zenon_H2c zenon_H28 zenon_H19b zenon_H20 zenon_H18f zenon_H195 zenon_H194 zenon_H186 zenon_H198 zenon_H175 zenon_H176 zenon_H174 zenon_H173 zenon_H172 zenon_H16f zenon_H16b zenon_H166 zenon_H165 zenon_H170 zenon_H152 zenon_H132 zenon_H137 zenon_H12e zenon_H13e zenon_H142 zenon_H13c zenon_H153 zenon_H154 zenon_H171 zenon_H177 zenon_H11f zenon_H122 zenon_H19c. % 4.69/4.87 apply (zenon_or_s _ _ zenon_H1b9); [ zenon_intro zenon_H29 | zenon_intro zenon_H145 ]. % 4.69/4.87 apply (zenon_L162_); trivial. % 4.69/4.87 apply (zenon_L199_); trivial. % 4.69/4.87 (* end of lemma zenon_L200_ *) % 4.69/4.87 assert (zenon_L201_ : ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (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 (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e0) (e0)) = (e1)))) -> False). % 4.69/4.87 do 0 intro. intros zenon_H1ba zenon_H19d zenon_Hc3 zenon_H1a7 zenon_H1ab zenon_H1b7 zenon_H1b6 zenon_H1b8 zenon_H1b9 zenon_H19a zenon_H11d zenon_H1e zenon_H1f zenon_H114 zenon_H113 zenon_H110 zenon_H104 zenon_He9 zenon_He6 zenon_Hdc zenon_Hda zenon_Hd7 zenon_Hdf zenon_Hd0 zenon_Hbe zenon_H102 zenon_Hf6 zenon_Hef zenon_Hf3 zenon_Hf9 zenon_H101 zenon_H103 zenon_Hfd zenon_H100 zenon_H7c zenon_H4b zenon_H4d zenon_H4c zenon_H46 zenon_H41 zenon_H94 zenon_H54 zenon_H117 zenon_H86 zenon_H89 zenon_H8f zenon_H82 zenon_H7b zenon_H6c zenon_H70 zenon_H75 zenon_He2 zenon_H96 zenon_H95 zenon_Hb3 zenon_Haf zenon_H9d zenon_Ha9 zenon_Ha4 zenon_Ha0 zenon_Hac zenon_Hb9 zenon_H118 zenon_H35 zenon_H36 zenon_H38 zenon_H33 zenon_H1d zenon_H11e zenon_H2c zenon_H28 zenon_H19b zenon_H20 zenon_H18f zenon_H195 zenon_H194 zenon_H186 zenon_H198 zenon_H175 zenon_H176 zenon_H174 zenon_H173 zenon_H172 zenon_H16f zenon_H16b zenon_H166 zenon_H165 zenon_H170 zenon_H152 zenon_H132 zenon_H137 zenon_H12e zenon_H13e zenon_H142 zenon_H13c zenon_H153 zenon_H154 zenon_H171 zenon_H177 zenon_H11f zenon_H122 zenon_H19c. % 4.69/4.87 apply (zenon_or_s _ _ zenon_H1ba); [ zenon_intro zenon_H29 | zenon_intro zenon_H179 ]. % 4.69/4.87 apply (zenon_L162_); trivial. % 4.69/4.87 apply (zenon_L200_); trivial. % 4.69/4.87 (* end of lemma zenon_L201_ *) % 4.69/4.87 assert (zenon_L202_ : ((~((op (e3) (e1)) = (e3)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (~((e1) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (e0))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (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 (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> False). % 4.69/4.87 do 0 intro. intros zenon_H19c zenon_H19a zenon_H122 zenon_H11f zenon_H177 zenon_H171 zenon_H154 zenon_H153 zenon_H13c zenon_H142 zenon_H13e zenon_H12e zenon_H137 zenon_H132 zenon_H152 zenon_H170 zenon_H165 zenon_H166 zenon_H16b zenon_H16f zenon_H172 zenon_H173 zenon_H174 zenon_H176 zenon_H175 zenon_H198 zenon_H186 zenon_H194 zenon_H195 zenon_H18f zenon_H20 zenon_H19b zenon_H28 zenon_H2c zenon_H29 zenon_H11d zenon_H1e zenon_H1f zenon_H114 zenon_H113 zenon_H110 zenon_H104 zenon_He9 zenon_He6 zenon_Hdc zenon_Hda zenon_Hd7 zenon_Hdf zenon_Hd0 zenon_Hbe zenon_H102 zenon_Hf6 zenon_Hef zenon_Hf3 zenon_Hf9 zenon_H101 zenon_H103 zenon_Hfd zenon_H100 zenon_H7c zenon_H4b zenon_H4d zenon_H4c zenon_H46 zenon_H41 zenon_H94 zenon_H54 zenon_H117 zenon_H86 zenon_H89 zenon_H8f zenon_H82 zenon_H7b zenon_H6c zenon_H70 zenon_H75 zenon_He2 zenon_H96 zenon_H95 zenon_Hb4 zenon_Hb3 zenon_Haf zenon_H9d zenon_Ha9 zenon_Ha4 zenon_Ha0 zenon_Hac zenon_Hb9 zenon_H118 zenon_H35 zenon_H36 zenon_H38 zenon_H33 zenon_H1d zenon_H11e. % 4.69/4.87 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H2a | zenon_intro zenon_H5b ]. % 4.69/4.87 apply (zenon_L72_); trivial. % 4.69/4.87 apply (zenon_L161_); trivial. % 4.69/4.87 (* end of lemma zenon_L202_ *) % 4.69/4.87 assert (zenon_L203_ : ((~((op (e3) (e1)) = (e3)))\/(~((op (e0) (e0)) = (e1)))) -> (((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))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (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))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e3) (e0)) = (op (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)))) -> (((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 (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> False). % 4.69/4.87 do 0 intro. intros zenon_H19c zenon_H1d zenon_H100 zenon_H82 zenon_H104 zenon_H1a7 zenon_Ha0 zenon_Ha4 zenon_H102 zenon_H179 zenon_H4c zenon_H4d zenon_H4b zenon_Hfd zenon_H54 zenon_H103 zenon_Hc3 zenon_H36 zenon_H19d zenon_H38 zenon_H33 zenon_Hb4 zenon_H35 zenon_H96 zenon_He2 zenon_H145 zenon_Hdc zenon_Hda zenon_Hd7 zenon_H70 zenon_H86 zenon_Hf9 zenon_H2c zenon_H75 zenon_Hd0 zenon_Hac zenon_H28 zenon_Hb3 zenon_H114 zenon_H20 zenon_H1f zenon_H1e zenon_H1b8 zenon_H1b6 zenon_H122 zenon_H177 zenon_H171 zenon_H154 zenon_H153 zenon_H113 zenon_H142 zenon_H117 zenon_H13e zenon_Hdf zenon_H12e zenon_Haf zenon_Ha9 zenon_H94 zenon_H7b zenon_H152 zenon_H170 zenon_Hbe zenon_H16b zenon_H16f zenon_H172 zenon_H173 zenon_H174 zenon_H176 zenon_H175 zenon_H19a zenon_He9 zenon_H9d zenon_H166 zenon_H132 zenon_H165 zenon_H1ab zenon_H11f zenon_H18f zenon_H118 zenon_Hb9 zenon_H41 zenon_H13c zenon_H137 zenon_H19b zenon_H1b7 zenon_H11e. % 4.69/4.87 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H2a | zenon_intro zenon_H5b ]. % 4.69/4.87 apply (zenon_L198_); trivial. % 4.69/4.87 apply (zenon_L194_); trivial. % 4.69/4.87 (* end of lemma zenon_L203_ *) % 4.69/4.87 assert (zenon_L204_ : ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e0) (e0)) = (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (((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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (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 (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e0) (e0)) = (e1)))) -> False). % 4.69/4.87 do 0 intro. intros zenon_H1b9 zenon_H1b7 zenon_H1ab zenon_H1b6 zenon_H1b8 zenon_H19d zenon_Hc3 zenon_H179 zenon_H1a7 zenon_H11e zenon_H1d zenon_H33 zenon_H38 zenon_H36 zenon_H35 zenon_H118 zenon_Hb9 zenon_Hac zenon_Ha0 zenon_Ha4 zenon_Ha9 zenon_H9d zenon_Haf zenon_Hb3 zenon_Hb4 zenon_H95 zenon_H96 zenon_He2 zenon_H75 zenon_H70 zenon_H6c zenon_H7b zenon_H82 zenon_H8f zenon_H89 zenon_H86 zenon_H117 zenon_H54 zenon_H94 zenon_H41 zenon_H46 zenon_H4c zenon_H4d zenon_H4b zenon_H7c zenon_H100 zenon_Hfd zenon_H103 zenon_H101 zenon_Hf9 zenon_Hf3 zenon_Hef zenon_Hf6 zenon_H102 zenon_Hbe zenon_Hd0 zenon_Hdf zenon_Hd7 zenon_Hda zenon_Hdc zenon_He6 zenon_He9 zenon_H104 zenon_H110 zenon_H113 zenon_H114 zenon_H1f zenon_H1e zenon_H11d zenon_H2c zenon_H28 zenon_H19b zenon_H20 zenon_H18f zenon_H195 zenon_H194 zenon_H186 zenon_H198 zenon_H175 zenon_H176 zenon_H174 zenon_H173 zenon_H172 zenon_H16f zenon_H16b zenon_H166 zenon_H165 zenon_H170 zenon_H152 zenon_H132 zenon_H137 zenon_H12e zenon_H13e zenon_H142 zenon_H13c zenon_H153 zenon_H154 zenon_H171 zenon_H177 zenon_H11f zenon_H122 zenon_H19a zenon_H19c. % 4.69/4.87 apply (zenon_or_s _ _ zenon_H1b9); [ zenon_intro zenon_H29 | zenon_intro zenon_H145 ]. % 4.69/4.87 apply (zenon_L202_); trivial. % 4.69/4.87 apply (zenon_L203_); trivial. % 4.69/4.87 (* end of lemma zenon_L204_ *) % 4.69/4.87 assert (zenon_L205_ : ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (((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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (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 (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e0) (e0)) = (e1)))) -> False). % 4.69/4.87 do 0 intro. intros zenon_H1ba zenon_H1a7 zenon_Hc3 zenon_H19d zenon_H1b8 zenon_H1b6 zenon_H1ab zenon_H1b7 zenon_H1b9 zenon_H11e zenon_H1d zenon_H33 zenon_H38 zenon_H36 zenon_H35 zenon_H118 zenon_Hb9 zenon_Hac zenon_Ha0 zenon_Ha4 zenon_Ha9 zenon_H9d zenon_Haf zenon_Hb3 zenon_Hb4 zenon_H95 zenon_H96 zenon_He2 zenon_H75 zenon_H70 zenon_H6c zenon_H7b zenon_H82 zenon_H8f zenon_H89 zenon_H86 zenon_H117 zenon_H54 zenon_H94 zenon_H41 zenon_H46 zenon_H4c zenon_H4d zenon_H4b zenon_H7c zenon_H100 zenon_Hfd zenon_H103 zenon_H101 zenon_Hf9 zenon_Hf3 zenon_Hef zenon_Hf6 zenon_H102 zenon_Hbe zenon_Hd0 zenon_Hdf zenon_Hd7 zenon_Hda zenon_Hdc zenon_He6 zenon_He9 zenon_H104 zenon_H110 zenon_H113 zenon_H114 zenon_H1f zenon_H1e zenon_H11d zenon_H2c zenon_H28 zenon_H19b zenon_H20 zenon_H18f zenon_H195 zenon_H194 zenon_H186 zenon_H198 zenon_H175 zenon_H176 zenon_H174 zenon_H173 zenon_H172 zenon_H16f zenon_H16b zenon_H166 zenon_H165 zenon_H170 zenon_H152 zenon_H132 zenon_H137 zenon_H12e zenon_H13e zenon_H142 zenon_H13c zenon_H153 zenon_H154 zenon_H171 zenon_H177 zenon_H11f zenon_H122 zenon_H19a zenon_H19c. % 4.69/4.87 apply (zenon_or_s _ _ zenon_H1ba); [ zenon_intro zenon_H29 | zenon_intro zenon_H179 ]. % 4.69/4.87 apply (zenon_L202_); trivial. % 4.69/4.87 apply (zenon_L204_); trivial. % 4.69/4.87 (* end of lemma zenon_L205_ *) % 4.69/4.87 assert (zenon_L206_ : ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (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))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (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 (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (e0))) -> (((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 (e2) (e0)) = (op (e2) (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 (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> False). % 4.69/4.87 do 0 intro. intros zenon_H1b7 zenon_H172 zenon_H16f zenon_H16b zenon_He9 zenon_H166 zenon_H86 zenon_H165 zenon_Hbe zenon_H170 zenon_H152 zenon_H1e zenon_H1f zenon_H114 zenon_H7b zenon_H132 zenon_H100 zenon_Hd0 zenon_H94 zenon_H5b zenon_H137 zenon_Hb4 zenon_Hac zenon_H82 zenon_Ha0 zenon_H4c zenon_Ha4 zenon_Ha9 zenon_H37 zenon_H9d zenon_Haf zenon_Hb3 zenon_H7c zenon_Hb9 zenon_H12e zenon_H76 zenon_H11f zenon_H118 zenon_H21 zenon_H1d zenon_Hdf zenon_H13e zenon_H117 zenon_H142 zenon_H70 zenon_H75 zenon_H113 zenon_H54 zenon_Hfd zenon_H13c zenon_H103 zenon_H153 zenon_H154 zenon_H171. % 4.69/4.87 apply (zenon_or_s _ _ zenon_H1b7); [ zenon_intro zenon_H36 | zenon_intro zenon_H36 ]. % 4.69/4.87 apply (zenon_L134_); trivial. % 4.69/4.87 apply (zenon_L134_); trivial. % 4.69/4.87 (* end of lemma zenon_L206_ *) % 4.69/4.87 assert (zenon_L207_ : ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (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)))) -> (((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 (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((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) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (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)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> False). % 4.69/4.88 do 0 intro. intros zenon_H174 zenon_H173 zenon_H171 zenon_H154 zenon_H153 zenon_H103 zenon_H13c zenon_Hfd zenon_H54 zenon_H113 zenon_H75 zenon_H70 zenon_H142 zenon_H117 zenon_H13e zenon_Hdf zenon_H1d zenon_H21 zenon_H118 zenon_H11f zenon_H76 zenon_H12e zenon_Hb9 zenon_Hb3 zenon_Haf zenon_H9d zenon_H37 zenon_Ha9 zenon_Ha4 zenon_H4c zenon_Ha0 zenon_H82 zenon_Hac zenon_Hb4 zenon_H137 zenon_H5b zenon_H94 zenon_Hd0 zenon_H100 zenon_H132 zenon_H7b zenon_H114 zenon_H1f zenon_H1e zenon_H152 zenon_H170 zenon_Hbe zenon_H165 zenon_H86 zenon_H166 zenon_He9 zenon_H16b zenon_H16f zenon_H172 zenon_H1b7. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H7c | zenon_intro zenon_Hc3 ]. % 4.69/4.88 apply (zenon_L206_); trivial. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H7c | zenon_intro zenon_H145 ]. % 4.69/4.88 apply (zenon_L206_); trivial. % 4.69/4.88 apply (zenon_L135_); trivial. % 4.69/4.88 (* end of lemma zenon_L207_ *) % 4.69/4.88 assert (zenon_L208_ : ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (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))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (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 (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (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 (e2) (e0)) = (op (e2) (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 (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> False). % 4.69/4.88 do 0 intro. intros zenon_H122 zenon_H1b7 zenon_H172 zenon_H16f zenon_H16b zenon_He9 zenon_H166 zenon_H86 zenon_H165 zenon_Hbe zenon_H170 zenon_H152 zenon_H1e zenon_H1f zenon_H114 zenon_H7b zenon_H132 zenon_H100 zenon_Hd0 zenon_H94 zenon_H5b zenon_H137 zenon_Hb4 zenon_Hac zenon_H82 zenon_Ha0 zenon_H4c zenon_Ha4 zenon_Ha9 zenon_H37 zenon_H9d zenon_Haf zenon_Hb3 zenon_Hb9 zenon_H12e zenon_H76 zenon_H11f zenon_H118 zenon_H1d zenon_Hdf zenon_H13e zenon_H117 zenon_H142 zenon_H70 zenon_H75 zenon_H113 zenon_H54 zenon_Hfd zenon_H13c zenon_H103 zenon_H153 zenon_H154 zenon_H171 zenon_H173 zenon_H174. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_H21 | zenon_intro zenon_H104 ]. % 4.69/4.88 apply (zenon_L207_); trivial. % 4.69/4.88 apply (zenon_L73_); trivial. % 4.69/4.88 (* end of lemma zenon_L208_ *) % 4.69/4.88 assert (zenon_L209_ : ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (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)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((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 (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (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)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> False). % 4.69/4.88 do 0 intro. intros zenon_H176 zenon_H174 zenon_H173 zenon_H171 zenon_H154 zenon_H153 zenon_H103 zenon_H13c zenon_Hfd zenon_H54 zenon_H113 zenon_H75 zenon_H70 zenon_H142 zenon_H117 zenon_H13e zenon_Hdf zenon_H118 zenon_H12e zenon_Hb9 zenon_Hb3 zenon_Haf zenon_H9d zenon_H37 zenon_Ha9 zenon_Ha4 zenon_H4c zenon_Ha0 zenon_H82 zenon_Hac zenon_H137 zenon_H94 zenon_Hd0 zenon_H100 zenon_H132 zenon_H7b zenon_H114 zenon_H152 zenon_H170 zenon_Hbe zenon_H165 zenon_H86 zenon_H166 zenon_He9 zenon_H16b zenon_H16f zenon_H172 zenon_H1b7 zenon_H1d zenon_H1f zenon_H1e zenon_H11f zenon_Hb4 zenon_H5b zenon_H122. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H20 | zenon_intro zenon_H76 ]. % 4.69/4.88 apply (zenon_L74_); trivial. % 4.69/4.88 apply (zenon_L208_); trivial. % 4.69/4.88 (* end of lemma zenon_L209_ *) % 4.69/4.88 assert (zenon_L210_ : ((~((op (e1) (e1)) = (e1)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (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))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (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 (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> False). % 4.69/4.88 do 0 intro. intros zenon_H1b8 zenon_H122 zenon_Hb4 zenon_H11f zenon_H1e zenon_H1f zenon_H1d zenon_H1b7 zenon_H172 zenon_H16f zenon_H16b zenon_He9 zenon_H166 zenon_H86 zenon_H165 zenon_Hbe zenon_H170 zenon_H152 zenon_H114 zenon_H7b zenon_H132 zenon_H100 zenon_Hd0 zenon_H94 zenon_H137 zenon_Hac zenon_H82 zenon_Ha0 zenon_H4c zenon_Ha4 zenon_Ha9 zenon_H9d zenon_Haf zenon_Hb3 zenon_Hb9 zenon_H12e zenon_H118 zenon_Hdf zenon_H13e zenon_H117 zenon_H142 zenon_H70 zenon_H75 zenon_H113 zenon_H54 zenon_Hfd zenon_H13c zenon_H103 zenon_H153 zenon_H154 zenon_H171 zenon_H173 zenon_H174 zenon_H176 zenon_Hc3 zenon_H37 zenon_H38 zenon_H33. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H1b8); [ zenon_intro zenon_H36 | zenon_intro zenon_H5b ]. % 4.69/4.88 apply (zenon_L189_); trivial. % 4.69/4.88 apply (zenon_L209_); trivial. % 4.69/4.88 (* end of lemma zenon_L210_ *) % 4.69/4.88 assert (zenon_L211_ : ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (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 (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e0) (e0)) = (e1)))) -> False). % 4.69/4.88 do 0 intro. intros zenon_H1bb zenon_H1b7 zenon_H1b8 zenon_H11d zenon_H1e zenon_H1f zenon_H114 zenon_H113 zenon_H110 zenon_H104 zenon_He9 zenon_He6 zenon_Hdc zenon_Hda zenon_Hd7 zenon_Hdf zenon_Hd0 zenon_Hbe zenon_H102 zenon_Hf6 zenon_Hef zenon_Hf3 zenon_Hf9 zenon_H101 zenon_H103 zenon_Hfd zenon_H100 zenon_H7c zenon_H4b zenon_H4d zenon_H4c zenon_H46 zenon_H41 zenon_H94 zenon_H54 zenon_H117 zenon_H86 zenon_H89 zenon_H8f zenon_H82 zenon_H7b zenon_H6c zenon_H70 zenon_H75 zenon_He2 zenon_H96 zenon_H95 zenon_Hb4 zenon_Hb3 zenon_Haf zenon_H9d zenon_Ha9 zenon_Ha4 zenon_Ha0 zenon_Hac zenon_Hb9 zenon_H118 zenon_H35 zenon_H36 zenon_H37 zenon_H38 zenon_H33 zenon_H1d zenon_H2c zenon_H28 zenon_H19b zenon_H20 zenon_H18f zenon_H195 zenon_H194 zenon_H186 zenon_H198 zenon_H175 zenon_H176 zenon_H174 zenon_H173 zenon_H172 zenon_H16f zenon_H16b zenon_H166 zenon_H165 zenon_H170 zenon_H152 zenon_H132 zenon_H137 zenon_H12e zenon_H13e zenon_H142 zenon_H13c zenon_H153 zenon_H154 zenon_H171 zenon_H177 zenon_H11f zenon_H122 zenon_H19a zenon_H19c. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H29 | zenon_intro zenon_Hc3 ]. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H2a | zenon_intro zenon_H5b ]. % 4.69/4.88 apply (zenon_L71_); trivial. % 4.69/4.88 apply (zenon_L161_); trivial. % 4.69/4.88 apply (zenon_L210_); trivial. % 4.69/4.88 (* end of lemma zenon_L211_ *) % 4.69/4.88 assert (zenon_L212_ : ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (~((e1) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (e0))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (((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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> False). % 4.69/4.88 do 0 intro. intros zenon_H1bc zenon_H19c zenon_H19a zenon_H122 zenon_H11f zenon_H177 zenon_H171 zenon_H154 zenon_H153 zenon_H13c zenon_H142 zenon_H13e zenon_H12e zenon_H137 zenon_H132 zenon_H152 zenon_H170 zenon_H165 zenon_H166 zenon_H16b zenon_H16f zenon_H172 zenon_H173 zenon_H174 zenon_H176 zenon_H175 zenon_H198 zenon_H186 zenon_H194 zenon_H195 zenon_H18f zenon_H20 zenon_H19b zenon_H28 zenon_H2c zenon_H1d zenon_H33 zenon_H38 zenon_H37 zenon_H36 zenon_H35 zenon_H118 zenon_Hb9 zenon_Hac zenon_Ha0 zenon_Ha4 zenon_Ha9 zenon_H9d zenon_Haf zenon_Hb3 zenon_Hb4 zenon_H95 zenon_H96 zenon_He2 zenon_H75 zenon_H70 zenon_H6c zenon_H7b zenon_H82 zenon_H8f zenon_H89 zenon_H86 zenon_H117 zenon_H54 zenon_H94 zenon_H41 zenon_H46 zenon_H4d zenon_H4b zenon_H7c zenon_H100 zenon_Hfd zenon_H103 zenon_H101 zenon_Hf9 zenon_Hf3 zenon_Hef zenon_Hf6 zenon_H102 zenon_Hbe zenon_Hd0 zenon_Hdf zenon_Hd7 zenon_Hda zenon_Hdc zenon_He6 zenon_He9 zenon_H104 zenon_H110 zenon_H113 zenon_H114 zenon_H1f zenon_H1e zenon_H11d zenon_H1b8 zenon_H1b7 zenon_H1bb. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H1bc); [ zenon_intro zenon_H4c | zenon_intro zenon_H4c ]. % 4.69/4.88 apply (zenon_L211_); trivial. % 4.69/4.88 apply (zenon_L211_); trivial. % 4.69/4.88 (* end of lemma zenon_L212_ *) % 4.69/4.88 assert (zenon_L213_ : ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (~((e1) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (e0))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (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 (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> False). % 4.69/4.88 do 0 intro. intros zenon_H1bd zenon_H1bc zenon_H19c zenon_H19a zenon_H122 zenon_H11f zenon_H177 zenon_H171 zenon_H154 zenon_H153 zenon_H13c zenon_H142 zenon_H13e zenon_H12e zenon_H137 zenon_H132 zenon_H152 zenon_H170 zenon_H165 zenon_H166 zenon_H16b zenon_H16f zenon_H172 zenon_H173 zenon_H174 zenon_H176 zenon_H175 zenon_H198 zenon_H186 zenon_H194 zenon_H195 zenon_H18f zenon_H20 zenon_H19b zenon_H28 zenon_H2c zenon_H11d zenon_H1e zenon_H1f zenon_H114 zenon_H113 zenon_H110 zenon_H104 zenon_He9 zenon_He6 zenon_Hdc zenon_Hda zenon_Hd7 zenon_Hdf zenon_Hd0 zenon_Hbe zenon_H102 zenon_Hf6 zenon_Hef zenon_Hf3 zenon_Hf9 zenon_H101 zenon_H103 zenon_Hfd zenon_H100 zenon_H7c zenon_H4b zenon_H4d zenon_H46 zenon_H41 zenon_H94 zenon_H54 zenon_H117 zenon_H86 zenon_H89 zenon_H8f zenon_H82 zenon_H7b zenon_H6c zenon_H70 zenon_H75 zenon_He2 zenon_H96 zenon_H95 zenon_Hb4 zenon_Hb3 zenon_Haf zenon_H9d zenon_Ha9 zenon_Ha4 zenon_Ha0 zenon_Hac zenon_Hb9 zenon_H118 zenon_H35 zenon_H36 zenon_H38 zenon_H33 zenon_H1d zenon_H11e zenon_H1ba zenon_H1a7 zenon_H19d zenon_H1b8 zenon_H1b6 zenon_H1ab zenon_H1b7 zenon_H1b9 zenon_H1bb. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H1bd); [ zenon_intro zenon_H4c | zenon_intro zenon_H37 ]. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H29 | zenon_intro zenon_Hc3 ]. % 4.69/4.88 apply (zenon_L202_); trivial. % 4.69/4.88 apply (zenon_L205_); trivial. % 4.69/4.88 apply (zenon_L212_); trivial. % 4.69/4.88 (* end of lemma zenon_L213_ *) % 4.69/4.88 assert (zenon_L214_ : ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (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)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((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 (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (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)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((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)) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (e0))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> False). % 4.69/4.88 do 0 intro. intros zenon_H1ba zenon_H38 zenon_Hc3 zenon_H1ab zenon_H41 zenon_H19a zenon_H122 zenon_H5b zenon_H11f zenon_H1e zenon_H1f zenon_H1d zenon_H177 zenon_H171 zenon_H154 zenon_H153 zenon_H103 zenon_H13c zenon_Hfd zenon_H54 zenon_H113 zenon_H75 zenon_H70 zenon_H142 zenon_H117 zenon_H13e zenon_Hdf zenon_H118 zenon_H12e zenon_Hb9 zenon_Hb3 zenon_Haf zenon_H9d zenon_Ha9 zenon_Ha4 zenon_Ha0 zenon_H82 zenon_Hac zenon_H137 zenon_H94 zenon_Hd0 zenon_H100 zenon_H36 zenon_H132 zenon_H7b zenon_H114 zenon_H152 zenon_H170 zenon_Hbe zenon_H165 zenon_H86 zenon_H166 zenon_He9 zenon_H16b zenon_H16f zenon_H172 zenon_H173 zenon_H174 zenon_H176 zenon_H175 zenon_H2c zenon_H28 zenon_H101 zenon_Hef zenon_H198 zenon_H7c zenon_H186 zenon_H4c zenon_H4d zenon_H4b zenon_H104 zenon_H194 zenon_Hf6 zenon_H195 zenon_H18f zenon_H20 zenon_H19b. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H1ba); [ zenon_intro zenon_H29 | zenon_intro zenon_H179 ]. % 4.69/4.88 apply (zenon_L161_); trivial. % 4.69/4.88 apply (zenon_L194_); trivial. % 4.69/4.88 (* end of lemma zenon_L214_ *) % 4.69/4.88 assert (zenon_L215_ : ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (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))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (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 (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> False). % 4.69/4.88 do 0 intro. intros zenon_H1b6 zenon_H19b zenon_H20 zenon_H18f zenon_H195 zenon_Hf6 zenon_H194 zenon_H104 zenon_H4b zenon_H4d zenon_H186 zenon_H7c zenon_H198 zenon_Hef zenon_H101 zenon_H28 zenon_H2c zenon_H175 zenon_H176 zenon_H174 zenon_H173 zenon_H172 zenon_H16f zenon_H16b zenon_He9 zenon_H166 zenon_H86 zenon_H165 zenon_Hbe zenon_H170 zenon_H152 zenon_H114 zenon_H7b zenon_H132 zenon_H36 zenon_H100 zenon_Hd0 zenon_H94 zenon_H137 zenon_Hac zenon_H82 zenon_Ha0 zenon_Ha4 zenon_Ha9 zenon_H9d zenon_Haf zenon_Hb3 zenon_Hb9 zenon_H12e zenon_H118 zenon_Hdf zenon_H13e zenon_H117 zenon_H142 zenon_H70 zenon_H75 zenon_H113 zenon_H54 zenon_Hfd zenon_H13c zenon_H103 zenon_H153 zenon_H154 zenon_H171 zenon_H177 zenon_H1d zenon_H1f zenon_H1e zenon_H11f zenon_H5b zenon_H122 zenon_H19a zenon_H1ba zenon_H38 zenon_H1ab zenon_H41 zenon_H1bb. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H4c | zenon_intro zenon_Hb4 ]. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H29 | zenon_intro zenon_Hc3 ]. % 4.69/4.88 apply (zenon_L161_); trivial. % 4.69/4.88 apply (zenon_L214_); trivial. % 4.69/4.88 apply (zenon_L138_); trivial. % 4.69/4.88 (* end of lemma zenon_L215_ *) % 4.69/4.88 assert (zenon_L216_ : ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (~((e1) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (e0))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (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 (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e0) (e0)) = (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> False). % 4.69/4.88 do 0 intro. intros zenon_H1bd zenon_H1bb zenon_H1bc zenon_H19c zenon_H19a zenon_H122 zenon_H11f zenon_H177 zenon_H171 zenon_H154 zenon_H153 zenon_H13c zenon_H142 zenon_H13e zenon_H12e zenon_H137 zenon_H132 zenon_H152 zenon_H170 zenon_H165 zenon_H166 zenon_H16b zenon_H16f zenon_H172 zenon_H173 zenon_H174 zenon_H176 zenon_H175 zenon_H198 zenon_H186 zenon_H194 zenon_H195 zenon_H18f zenon_H20 zenon_H19b zenon_H28 zenon_H2c zenon_H11d zenon_H1e zenon_H1f zenon_H114 zenon_H113 zenon_H110 zenon_H104 zenon_He9 zenon_He6 zenon_Hdc zenon_Hda zenon_Hd7 zenon_Hdf zenon_Hd0 zenon_Hbe zenon_H102 zenon_Hf6 zenon_Hef zenon_Hf3 zenon_Hf9 zenon_H101 zenon_H103 zenon_Hfd zenon_H100 zenon_H7c zenon_H4b zenon_H4d zenon_H46 zenon_H41 zenon_H94 zenon_H54 zenon_H117 zenon_H86 zenon_H89 zenon_H8f zenon_H82 zenon_H7b zenon_H6c zenon_H70 zenon_H75 zenon_He2 zenon_H96 zenon_H95 zenon_Hb4 zenon_Hb3 zenon_Haf zenon_H9d zenon_Ha9 zenon_Ha4 zenon_Ha0 zenon_Hac zenon_Hb9 zenon_H118 zenon_H35 zenon_H36 zenon_H38 zenon_H33 zenon_H1d zenon_H11e zenon_H1b9 zenon_H1b7 zenon_H1ab zenon_H1b6 zenon_H1b8 zenon_H19d zenon_Hc3 zenon_H1a7 zenon_H1ba. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H1bd); [ zenon_intro zenon_H4c | zenon_intro zenon_H37 ]. % 4.69/4.88 apply (zenon_L205_); trivial. % 4.69/4.88 apply (zenon_L212_); trivial. % 4.69/4.88 (* end of lemma zenon_L216_ *) % 4.69/4.88 assert (zenon_L217_ : ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (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))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (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 (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e3))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> False). % 4.69/4.88 do 0 intro. intros zenon_H1b6 zenon_H19b zenon_H20 zenon_H18f zenon_H195 zenon_Hf6 zenon_H194 zenon_H104 zenon_H4b zenon_H4d zenon_H186 zenon_H7c zenon_H198 zenon_Hef zenon_H101 zenon_H28 zenon_H2c zenon_H175 zenon_H176 zenon_H174 zenon_H173 zenon_H172 zenon_H16f zenon_H16b zenon_He9 zenon_H166 zenon_H86 zenon_H165 zenon_Hbe zenon_H170 zenon_H152 zenon_H114 zenon_H7b zenon_H132 zenon_H36 zenon_H100 zenon_Hd0 zenon_H94 zenon_H137 zenon_Hac zenon_H82 zenon_Ha0 zenon_Ha4 zenon_Ha9 zenon_H9d zenon_Haf zenon_Hb3 zenon_Hb9 zenon_H12e zenon_H118 zenon_Hdf zenon_H13e zenon_H117 zenon_H142 zenon_H70 zenon_H75 zenon_H113 zenon_H54 zenon_Hfd zenon_H13c zenon_H103 zenon_H153 zenon_H154 zenon_H171 zenon_H177 zenon_H1d zenon_H1f zenon_H1e zenon_H11f zenon_H5b zenon_H122 zenon_H19a zenon_H41 zenon_H1ab zenon_Hc3 zenon_H38 zenon_H1ba. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H4c | zenon_intro zenon_Hb4 ]. % 4.69/4.88 apply (zenon_L214_); trivial. % 4.69/4.88 apply (zenon_L73_); trivial. % 4.69/4.88 (* end of lemma zenon_L217_ *) % 4.69/4.88 assert (zenon_L218_ : ((~((op (e0) (e3)) = (e0)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e3))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (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)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((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 (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (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)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 4.69/4.88 do 0 intro. intros zenon_H1be zenon_H1bf zenon_H1bb zenon_H41 zenon_H1ab zenon_H38 zenon_H1ba zenon_H19a zenon_H122 zenon_H5b zenon_H11f zenon_H177 zenon_H171 zenon_H154 zenon_H153 zenon_H103 zenon_H13c zenon_Hfd zenon_H54 zenon_H113 zenon_H75 zenon_H70 zenon_H142 zenon_H117 zenon_H13e zenon_Hdf zenon_H118 zenon_H12e zenon_Hb9 zenon_Hb3 zenon_Haf zenon_H9d zenon_Ha9 zenon_Ha4 zenon_Ha0 zenon_H82 zenon_Hac zenon_H137 zenon_H94 zenon_Hd0 zenon_H100 zenon_H36 zenon_H132 zenon_H7b zenon_H114 zenon_H152 zenon_H170 zenon_Hbe zenon_H165 zenon_H86 zenon_H166 zenon_He9 zenon_H16b zenon_H16f zenon_H172 zenon_H173 zenon_H174 zenon_H176 zenon_H175 zenon_H28 zenon_H101 zenon_Hef zenon_H198 zenon_H186 zenon_H4d zenon_H4b zenon_H104 zenon_H194 zenon_Hf6 zenon_H18f zenon_H19b zenon_H1b6 zenon_H1c0 zenon_H1e zenon_H1f zenon_H20 zenon_H1d. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H1be); [ zenon_intro zenon_H21 | zenon_intro zenon_H2c ]. % 4.69/4.88 apply (zenon_L1_); trivial. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H7c | zenon_intro zenon_Hc3 ]. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H1bf); [ zenon_intro zenon_H195 | zenon_intro zenon_Hb4 ]. % 4.69/4.88 apply (zenon_L215_); trivial. % 4.69/4.88 apply (zenon_L73_); trivial. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H1c0); [ zenon_intro zenon_H7c | zenon_intro zenon_H179 ]. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H1bf); [ zenon_intro zenon_H195 | zenon_intro zenon_Hb4 ]. % 4.69/4.88 apply (zenon_L217_); trivial. % 4.69/4.88 apply (zenon_L138_); trivial. % 4.69/4.88 apply (zenon_L195_); trivial. % 4.69/4.88 (* end of lemma zenon_L218_ *) % 4.69/4.88 assert (zenon_L219_ : ((~((op (e0) (e3)) = (e0)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (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)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((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 (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (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)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e2) (e2)) = (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 4.69/4.88 do 0 intro. intros zenon_H1c1 zenon_H1be zenon_H1bf zenon_H1bb zenon_H41 zenon_H1ab zenon_H1ba zenon_H19a zenon_H122 zenon_H5b zenon_H11f zenon_H177 zenon_H171 zenon_H154 zenon_H153 zenon_H103 zenon_H13c zenon_Hfd zenon_H54 zenon_H113 zenon_H75 zenon_H70 zenon_H142 zenon_H117 zenon_H13e zenon_Hdf zenon_H118 zenon_H12e zenon_Hb9 zenon_Hb3 zenon_Haf zenon_H9d zenon_Ha9 zenon_Ha4 zenon_Ha0 zenon_H82 zenon_Hac zenon_H137 zenon_H94 zenon_Hd0 zenon_H100 zenon_H36 zenon_H132 zenon_H7b zenon_H114 zenon_H152 zenon_H170 zenon_Hbe zenon_H165 zenon_H86 zenon_H166 zenon_He9 zenon_H16b zenon_H16f zenon_H172 zenon_H173 zenon_H174 zenon_H176 zenon_H175 zenon_H28 zenon_H101 zenon_Hef zenon_H198 zenon_H186 zenon_H4b zenon_H104 zenon_H194 zenon_Hf6 zenon_H18f zenon_H19b zenon_H1b6 zenon_H1c0 zenon_H1c2 zenon_H1e zenon_H1f zenon_H20 zenon_H1d. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H1c1); [ zenon_intro zenon_H21 | zenon_intro zenon_H38 ]. % 4.69/4.88 apply (zenon_L1_); trivial. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H1c2); [ zenon_intro zenon_H21 | zenon_intro zenon_H4d ]. % 4.69/4.88 apply (zenon_L1_); trivial. % 4.69/4.88 apply (zenon_L218_); trivial. % 4.69/4.88 (* end of lemma zenon_L219_ *) % 4.69/4.88 assert (zenon_L220_ : ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (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))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (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 (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e1) (e1)) = (e3)))) -> False). % 4.69/4.88 do 0 intro. intros zenon_H1b7 zenon_H1d zenon_H20 zenon_H1f zenon_H1e zenon_H1c2 zenon_H1c0 zenon_H1b6 zenon_H19b zenon_H18f zenon_Hf6 zenon_H194 zenon_H104 zenon_H4b zenon_H186 zenon_H198 zenon_Hef zenon_H101 zenon_H28 zenon_H175 zenon_H176 zenon_H174 zenon_H173 zenon_H172 zenon_H16f zenon_H16b zenon_He9 zenon_H166 zenon_H86 zenon_H165 zenon_Hbe zenon_H170 zenon_H152 zenon_H114 zenon_H7b zenon_H132 zenon_H100 zenon_Hd0 zenon_H94 zenon_H137 zenon_Hac zenon_H82 zenon_Ha0 zenon_Ha4 zenon_Ha9 zenon_H9d zenon_Haf zenon_Hb3 zenon_Hb9 zenon_H12e zenon_H118 zenon_Hdf zenon_H13e zenon_H117 zenon_H142 zenon_H70 zenon_H75 zenon_H113 zenon_H54 zenon_Hfd zenon_H13c zenon_H103 zenon_H153 zenon_H154 zenon_H171 zenon_H177 zenon_H11f zenon_H5b zenon_H122 zenon_H19a zenon_H1ba zenon_H1ab zenon_H41 zenon_H1bb zenon_H1bf zenon_H1be zenon_H1c1. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H1b7); [ zenon_intro zenon_H36 | zenon_intro zenon_H36 ]. % 4.69/4.88 apply (zenon_L219_); trivial. % 4.69/4.88 apply (zenon_L219_); trivial. % 4.69/4.88 (* end of lemma zenon_L220_ *) % 4.69/4.88 assert (zenon_L221_ : ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (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))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (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 (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> False). % 4.69/4.88 do 0 intro. intros zenon_H177 zenon_H1b7 zenon_H172 zenon_H16f zenon_H16b zenon_He9 zenon_H166 zenon_H86 zenon_H165 zenon_Hbe zenon_H170 zenon_H152 zenon_H114 zenon_H7b zenon_H132 zenon_H100 zenon_Hd0 zenon_H94 zenon_H137 zenon_Hac zenon_H82 zenon_Ha0 zenon_Ha4 zenon_Ha9 zenon_H37 zenon_H9d zenon_Haf zenon_Hb3 zenon_Hb9 zenon_H12e zenon_H118 zenon_Hdf zenon_H13e zenon_H117 zenon_H142 zenon_H70 zenon_H75 zenon_H113 zenon_H54 zenon_Hfd zenon_H13c zenon_H103 zenon_H153 zenon_H154 zenon_H171 zenon_H173 zenon_H174 zenon_H176 zenon_H1d zenon_H1f zenon_H1e zenon_H11f zenon_Hb4 zenon_H5b zenon_H122. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_H20 | zenon_intro zenon_H4c ]. % 4.69/4.88 apply (zenon_L74_); trivial. % 4.69/4.88 apply (zenon_L209_); trivial. % 4.69/4.88 (* end of lemma zenon_L221_ *) % 4.69/4.88 assert (zenon_L222_ : ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (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)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((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 (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (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)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> False). % 4.69/4.88 do 0 intro. intros zenon_H175 zenon_H176 zenon_H174 zenon_H173 zenon_H171 zenon_H154 zenon_H153 zenon_H103 zenon_H13c zenon_Hfd zenon_H54 zenon_H113 zenon_H75 zenon_H70 zenon_H142 zenon_H117 zenon_H13e zenon_Hdf zenon_H118 zenon_H12e zenon_Hb9 zenon_Hb3 zenon_Haf zenon_H9d zenon_Ha9 zenon_Ha4 zenon_Ha0 zenon_H82 zenon_Hac zenon_H137 zenon_H94 zenon_Hd0 zenon_H100 zenon_H132 zenon_H7b zenon_H114 zenon_H152 zenon_H170 zenon_Hbe zenon_H165 zenon_H86 zenon_H166 zenon_He9 zenon_H16b zenon_H16f zenon_H172 zenon_H1b7 zenon_H177 zenon_H1d zenon_H1f zenon_H1e zenon_H11f zenon_Hb4 zenon_H5b zenon_H122. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H20 | zenon_intro zenon_H37 ]. % 4.69/4.88 apply (zenon_L74_); trivial. % 4.69/4.88 apply (zenon_L221_); trivial. % 4.69/4.88 (* end of lemma zenon_L222_ *) % 4.69/4.88 assert (zenon_L223_ : ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (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))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (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 (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e1) (e1)) = (e3)))) -> False). % 4.69/4.88 do 0 intro. intros zenon_H1c3 zenon_H1d zenon_H1f zenon_H1e zenon_H1b7 zenon_H1c2 zenon_H1c0 zenon_H1b6 zenon_H19b zenon_H18f zenon_Hf6 zenon_H194 zenon_H4b zenon_H186 zenon_H198 zenon_Hef zenon_H101 zenon_H28 zenon_H175 zenon_H176 zenon_H174 zenon_H173 zenon_H172 zenon_H16f zenon_H16b zenon_He9 zenon_H166 zenon_H86 zenon_H165 zenon_Hbe zenon_H170 zenon_H152 zenon_H114 zenon_H7b zenon_H132 zenon_H100 zenon_Hd0 zenon_H94 zenon_H137 zenon_Hac zenon_H82 zenon_Ha0 zenon_Ha4 zenon_Ha9 zenon_H9d zenon_Haf zenon_Hb3 zenon_Hb9 zenon_H12e zenon_H118 zenon_Hdf zenon_H13e zenon_H117 zenon_H142 zenon_H70 zenon_H75 zenon_H113 zenon_H54 zenon_Hfd zenon_H13c zenon_H103 zenon_H153 zenon_H154 zenon_H171 zenon_H177 zenon_H11f zenon_H5b zenon_H122 zenon_H19a zenon_H1ba zenon_H1ab zenon_H41 zenon_H1bb zenon_H1bf zenon_H1be zenon_H1c1. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H20 | zenon_intro zenon_Hb4 ]. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_H21 | zenon_intro zenon_H104 ]. % 4.69/4.88 apply (zenon_L1_); trivial. % 4.69/4.88 apply (zenon_L220_); trivial. % 4.69/4.88 apply (zenon_L222_); trivial. % 4.69/4.88 (* end of lemma zenon_L223_ *) % 4.69/4.88 assert (zenon_L224_ : ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (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 (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> False). % 4.69/4.88 do 0 intro. intros zenon_H175 zenon_H176 zenon_H173 zenon_H170 zenon_H16b zenon_H16c zenon_H152 zenon_H114 zenon_H7b zenon_H132 zenon_H36 zenon_H100 zenon_Hd0 zenon_H94 zenon_H137 zenon_Hac zenon_H82 zenon_Ha0 zenon_Ha4 zenon_Ha9 zenon_H9d zenon_Haf zenon_Hb3 zenon_Hb9 zenon_H12e zenon_H118 zenon_Hdf zenon_H13e zenon_H117 zenon_H142 zenon_H70 zenon_H75 zenon_H113 zenon_H54 zenon_Hfd zenon_H13c zenon_H103 zenon_H153 zenon_H154 zenon_H171 zenon_H177 zenon_H1d zenon_H1f zenon_H1e zenon_H11f zenon_Hb4 zenon_H5b zenon_H122. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H20 | zenon_intro zenon_H37 ]. % 4.69/4.88 apply (zenon_L74_); trivial. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_H20 | zenon_intro zenon_H4c ]. % 4.69/4.88 apply (zenon_L74_); trivial. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H20 | zenon_intro zenon_H76 ]. % 4.69/4.88 apply (zenon_L74_); trivial. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_H21 | zenon_intro zenon_H104 ]. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H7c | zenon_intro zenon_H145 ]. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H135 | zenon_intro zenon_H104 ]. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H95 | zenon_intro zenon_H145 ]. % 4.69/4.88 apply (zenon_L109_); trivial. % 4.69/4.88 apply (zenon_L131_); trivial. % 4.69/4.88 apply (zenon_L73_); trivial. % 4.69/4.88 apply (zenon_L131_); trivial. % 4.69/4.88 apply (zenon_L73_); trivial. % 4.69/4.88 (* end of lemma zenon_L224_ *) % 4.69/4.88 assert (zenon_L225_ : ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (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)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (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 (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> (~((op (e0) (e1)) = (e0))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> False). % 4.69/4.88 do 0 intro. intros zenon_H1bf zenon_H1ba zenon_H1d zenon_H20 zenon_H5b zenon_Hb9 zenon_H137 zenon_H18f zenon_H82 zenon_H9d zenon_H103 zenon_Hfd zenon_Hf6 zenon_H194 zenon_H54 zenon_H100 zenon_H104 zenon_H4b zenon_H4d zenon_H16c zenon_H13c zenon_H186 zenon_H7c zenon_H198 zenon_H36 zenon_Hef zenon_H28 zenon_H2c zenon_H101 zenon_H118 zenon_H1e zenon_H11f zenon_H19a zenon_H175 zenon_H176 zenon_H173 zenon_H170 zenon_H16b zenon_H152 zenon_H114 zenon_H7b zenon_H132 zenon_Hd0 zenon_H94 zenon_Hac zenon_Ha0 zenon_Ha4 zenon_Ha9 zenon_Haf zenon_Hb3 zenon_H12e zenon_Hdf zenon_H13e zenon_H117 zenon_H142 zenon_H70 zenon_H75 zenon_H113 zenon_H153 zenon_H154 zenon_H171 zenon_H177 zenon_H1f zenon_H122 zenon_H1b6. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H1bf); [ zenon_intro zenon_H195 | zenon_intro zenon_Hb4 ]. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H4c | zenon_intro zenon_Hb4 ]. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H1ba); [ zenon_intro zenon_H29 | zenon_intro zenon_H179 ]. % 4.69/4.88 apply (zenon_L160_); trivial. % 4.69/4.88 apply (zenon_L193_); trivial. % 4.69/4.88 apply (zenon_L224_); trivial. % 4.69/4.88 apply (zenon_L73_); trivial. % 4.69/4.88 (* end of lemma zenon_L225_ *) % 4.69/4.88 assert (zenon_L226_ : ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (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)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((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 (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> False). % 4.69/4.88 do 0 intro. intros zenon_H1b6 zenon_H122 zenon_H5b zenon_H11f zenon_H1e zenon_H1f zenon_H1d zenon_H177 zenon_H171 zenon_H154 zenon_H153 zenon_H103 zenon_H13c zenon_Hfd zenon_H54 zenon_H113 zenon_H75 zenon_H70 zenon_H142 zenon_H117 zenon_H13e zenon_Hdf zenon_H118 zenon_H12e zenon_Hb9 zenon_Hb3 zenon_Haf zenon_H9d zenon_Ha9 zenon_Ha4 zenon_Ha0 zenon_H82 zenon_Hac zenon_H137 zenon_H94 zenon_Hd0 zenon_H100 zenon_H36 zenon_H132 zenon_H7b zenon_H114 zenon_H152 zenon_H16b zenon_H170 zenon_H173 zenon_H176 zenon_H175 zenon_H179 zenon_H16c zenon_H4d zenon_H4b. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H4c | zenon_intro zenon_Hb4 ]. % 4.69/4.88 apply (zenon_L193_); trivial. % 4.69/4.88 apply (zenon_L224_); trivial. % 4.69/4.88 (* end of lemma zenon_L226_ *) % 4.69/4.88 assert (zenon_L227_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> False). % 4.69/4.88 do 0 intro. intros zenon_H7b zenon_H7c zenon_H36 zenon_H195 zenon_H135. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H7b); [ zenon_intro zenon_H7e | zenon_intro zenon_H7d ]. % 4.69/4.88 exact (zenon_H7c zenon_H7e). % 4.69/4.88 apply (zenon_or_s _ _ zenon_H7d); [ zenon_intro zenon_H3e | zenon_intro zenon_H7f ]. % 4.69/4.88 exact (zenon_H36 zenon_H3e). % 4.69/4.88 apply (zenon_or_s _ _ zenon_H7f); [ zenon_intro zenon_H47 | zenon_intro zenon_H71 ]. % 4.69/4.88 exact (zenon_H195 zenon_H47). % 4.69/4.88 exact (zenon_H135 zenon_H71). % 4.69/4.88 (* end of lemma zenon_L227_ *) % 4.69/4.88 assert (zenon_L228_ : ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (~((e1) = (e3))) -> (~((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 (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (e1))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 4.69/4.88 do 0 intro. intros zenon_H1c4 zenon_H1e zenon_H118 zenon_H101 zenon_H28 zenon_Hef zenon_H36 zenon_H198 zenon_H7c zenon_H186 zenon_H29 zenon_H13c zenon_H16c zenon_H4c zenon_H4d zenon_H4b zenon_H104 zenon_H100 zenon_H54 zenon_H194 zenon_Hf6 zenon_H195 zenon_Hfd zenon_H103 zenon_H9d zenon_H82 zenon_H2b zenon_H18f zenon_H137 zenon_Hb9 zenon_H5b zenon_H20 zenon_H1d. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H2c | zenon_intro zenon_H2c ]. % 4.69/4.88 apply (zenon_L159_); trivial. % 4.69/4.88 apply (zenon_L159_); trivial. % 4.69/4.88 (* end of lemma zenon_L228_ *) % 4.69/4.88 assert (zenon_L229_ : ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((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 (e2) (e2)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (e3))) -> (~((e1) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 4.69/4.88 do 0 intro. intros zenon_H1c5 zenon_H18f zenon_H82 zenon_H9d zenon_Hfd zenon_H54 zenon_H100 zenon_H4b zenon_H4c zenon_H186 zenon_H1c4 zenon_H1e zenon_H118 zenon_H101 zenon_H29 zenon_H13c zenon_H2b zenon_H28 zenon_Hef zenon_H103 zenon_H195 zenon_H16c zenon_Hf6 zenon_H194 zenon_H198 zenon_H104 zenon_H137 zenon_H7c zenon_H36 zenon_H132 zenon_H135 zenon_H7b zenon_Hb9 zenon_H5b zenon_H20 zenon_H21 zenon_H1d. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H2c | zenon_intro zenon_H4d ]. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ]. % 4.69/4.88 exact (zenon_H1e zenon_H23). % 4.69/4.88 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ]. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H5a | zenon_intro zenon_H119 ]. % 4.69/4.88 exact (zenon_H5b zenon_H5a). % 4.69/4.88 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H9c | zenon_intro zenon_H11c ]. % 4.69/4.88 apply (zenon_L92_); trivial. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H87 ]. % 4.69/4.88 apply (zenon_L88_); trivial. % 4.69/4.88 apply (zenon_L157_); trivial. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H24); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 4.69/4.88 exact (zenon_H20 zenon_H27). % 4.69/4.88 exact (zenon_H21 zenon_H26). % 4.69/4.88 apply (zenon_L228_); trivial. % 4.69/4.88 (* end of lemma zenon_L229_ *) % 4.69/4.88 assert (zenon_L230_ : (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e2)) -> ((op (e3) (e3)) = (e2)) -> False). % 4.69/4.88 do 0 intro. intros zenon_H113 zenon_Hb0 zenon_H79. % 4.69/4.88 cut (((op (e3) (e0)) = (e2)) = ((op (e3) (e0)) = (op (e3) (e3)))). % 4.69/4.88 intro zenon_D_pnotp. % 4.69/4.88 apply zenon_H113. % 4.69/4.88 rewrite <- zenon_D_pnotp. % 4.69/4.88 exact zenon_Hb0. % 4.69/4.88 cut (((e2) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1aa]. % 4.69/4.88 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 4.69/4.88 congruence. % 4.69/4.88 apply zenon_Hb2. apply refl_equal. % 4.69/4.88 apply zenon_H1aa. apply sym_equal. exact zenon_H79. % 4.69/4.88 (* end of lemma zenon_L230_ *) % 4.69/4.88 assert (zenon_L231_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 4.69/4.88 do 0 intro. intros zenon_H103 zenon_Hb0 zenon_H113 zenon_H85 zenon_H9d zenon_H12e zenon_H54 zenon_H25 zenon_Hfd zenon_H92 zenon_H87 zenon_H13c. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_H108 | zenon_intro zenon_H107 ]. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H8a | zenon_intro zenon_H12f ]. % 4.69/4.88 apply (zenon_L79_); trivial. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H130 ]. % 4.69/4.88 apply (zenon_L81_); trivial. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H81 | zenon_intro zenon_H79 ]. % 4.69/4.88 exact (zenon_H85 zenon_H81). % 4.69/4.88 apply (zenon_L230_); trivial. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H109 ]. % 4.69/4.88 apply (zenon_L94_); trivial. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Hed | zenon_intro zenon_H8c ]. % 4.69/4.88 apply (zenon_L62_); trivial. % 4.69/4.88 apply (zenon_L95_); trivial. % 4.69/4.88 (* end of lemma zenon_L231_ *) % 4.69/4.88 assert (zenon_L232_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> False). % 4.69/4.88 do 0 intro. intros zenon_H7b zenon_H9d zenon_Ha1 zenon_H36 zenon_H195 zenon_H135. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H7b); [ zenon_intro zenon_H7e | zenon_intro zenon_H7d ]. % 4.69/4.88 apply (zenon_L118_); trivial. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H7d); [ zenon_intro zenon_H3e | zenon_intro zenon_H7f ]. % 4.69/4.88 exact (zenon_H36 zenon_H3e). % 4.69/4.88 apply (zenon_or_s _ _ zenon_H7f); [ zenon_intro zenon_H47 | zenon_intro zenon_H71 ]. % 4.69/4.88 exact (zenon_H195 zenon_H47). % 4.69/4.88 exact (zenon_H135 zenon_H71). % 4.69/4.88 (* end of lemma zenon_L232_ *) % 4.69/4.88 assert (zenon_L233_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e0)) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 4.69/4.88 do 0 intro. intros zenon_Hb3 zenon_Hb4 zenon_H135 zenon_H195 zenon_H36 zenon_H7b zenon_H82 zenon_H42 zenon_H123 zenon_H9d. % 4.69/4.88 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hb5 ]. % 4.69/4.88 exact (zenon_Hb4 zenon_Hb6). % 4.69/4.88 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hb7 ]. % 4.69/4.88 apply (zenon_L232_); trivial. % 4.69/4.88 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H98 | zenon_intro zenon_Hb0 ]. % 4.69/4.88 apply (zenon_L31_); trivial. % 4.69/4.88 apply (zenon_L77_); trivial. % 4.69/4.88 (* end of lemma zenon_L233_ *) % 4.69/4.88 assert (zenon_L234_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> False). % 4.69/4.88 do 0 intro. intros zenon_H28 zenon_H54 zenon_Hbd zenon_H13c zenon_Hfa zenon_H2b zenon_H2c. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2e | zenon_intro zenon_H2d ]. % 4.69/4.88 apply (zenon_L187_); trivial. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H30 | zenon_intro zenon_H2f ]. % 4.69/4.88 apply (zenon_L153_); trivial. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 4.69/4.88 exact (zenon_H2b zenon_H32). % 4.69/4.88 exact (zenon_H2c zenon_H31). % 4.69/4.88 (* end of lemma zenon_L234_ *) % 4.69/4.88 assert (zenon_L235_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((e1) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> False). % 4.69/4.88 do 0 intro. intros zenon_H101 zenon_Hb9 zenon_H25 zenon_H36 zenon_Hf0 zenon_Hef zenon_H28 zenon_H54 zenon_Hbd zenon_H13c zenon_H2b zenon_H2c. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H9c | zenon_intro zenon_H10a ]. % 4.69/4.88 apply (zenon_L92_); trivial. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H10a); [ zenon_intro zenon_H3e | zenon_intro zenon_H10b ]. % 4.69/4.88 exact (zenon_H36 zenon_H3e). % 4.69/4.88 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hfa ]. % 4.69/4.88 apply (zenon_L54_); trivial. % 4.69/4.88 apply (zenon_L234_); trivial. % 4.69/4.88 (* end of lemma zenon_L235_ *) % 4.69/4.88 assert (zenon_L236_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((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 (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 4.69/4.88 do 0 intro. intros zenon_H137 zenon_H5b zenon_H7c zenon_H2c zenon_H2b zenon_H13c zenon_H54 zenon_H28 zenon_Hef zenon_H36 zenon_H25 zenon_H101 zenon_Hbd zenon_Hb9. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_H5a | zenon_intro zenon_H138 ]. % 4.69/4.88 exact (zenon_H5b zenon_H5a). % 4.69/4.88 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_H7e | zenon_intro zenon_H139 ]. % 4.69/4.88 exact (zenon_H7c zenon_H7e). % 4.69/4.88 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H123 ]. % 4.69/4.88 apply (zenon_L235_); trivial. % 4.69/4.88 apply (zenon_L86_); trivial. % 4.69/4.88 (* end of lemma zenon_L236_ *) % 4.69/4.88 assert (zenon_L237_ : (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e2)) = (e2)) -> False). % 4.69/4.88 do 0 intro. intros zenon_H132 zenon_H92 zenon_Ha2. % 4.69/4.88 cut (((op (e0) (e2)) = (e2)) = ((op (e0) (e2)) = (op (e1) (e2)))). % 4.69/4.88 intro zenon_D_pnotp. % 4.69/4.88 apply zenon_H132. % 4.69/4.88 rewrite <- zenon_D_pnotp. % 4.69/4.88 exact zenon_H92. % 4.69/4.88 cut (((e2) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 4.69/4.88 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H134]. % 4.69/4.88 congruence. % 4.69/4.88 apply zenon_H134. apply refl_equal. % 4.69/4.88 apply zenon_Ha3. apply sym_equal. exact zenon_Ha2. % 4.69/4.88 (* end of lemma zenon_L237_ *) % 4.69/4.88 assert (zenon_L238_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (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) (e1)) = (e0)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 4.69/4.88 do 0 intro. intros zenon_H103 zenon_H132 zenon_H37 zenon_H7e zenon_H9d zenon_H165 zenon_H54 zenon_H25 zenon_Hfd zenon_H92 zenon_H87 zenon_H13c. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_H108 | zenon_intro zenon_H107 ]. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_Ha1 | zenon_intro zenon_H167 ]. % 4.69/4.88 apply (zenon_L118_); trivial. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H167); [ zenon_intro zenon_H40 | zenon_intro zenon_H168 ]. % 4.69/4.88 exact (zenon_H37 zenon_H40). % 4.69/4.88 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hd8 ]. % 4.69/4.88 apply (zenon_L237_); trivial. % 4.69/4.88 apply (zenon_L81_); trivial. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H109 ]. % 4.69/4.88 apply (zenon_L94_); trivial. % 4.69/4.88 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Hed | zenon_intro zenon_H8c ]. % 4.69/4.88 apply (zenon_L62_); trivial. % 4.69/4.88 apply (zenon_L95_); trivial. % 4.69/4.88 (* end of lemma zenon_L238_ *) % 4.69/4.88 assert (zenon_L239_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 4.69/4.89 do 0 intro. intros zenon_H100 zenon_Hb4 zenon_H82 zenon_H135 zenon_H195 zenon_H36 zenon_H103 zenon_H132 zenon_H37 zenon_H165 zenon_H54 zenon_H25 zenon_Hfd zenon_H13c zenon_H7b zenon_H87 zenon_H9d. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hb6 | zenon_intro zenon_H105 ]. % 4.69/4.89 exact (zenon_Hb4 zenon_Hb6). % 4.69/4.89 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H5e | zenon_intro zenon_H106 ]. % 4.69/4.89 apply (zenon_L148_); trivial. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_H92 | zenon_intro zenon_H8a ]. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H7b); [ zenon_intro zenon_H7e | zenon_intro zenon_H7d ]. % 4.69/4.89 apply (zenon_L238_); trivial. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H7d); [ zenon_intro zenon_H3e | zenon_intro zenon_H7f ]. % 4.69/4.89 exact (zenon_H36 zenon_H3e). % 4.69/4.89 apply (zenon_or_s _ _ zenon_H7f); [ zenon_intro zenon_H47 | zenon_intro zenon_H71 ]. % 4.69/4.89 exact (zenon_H195 zenon_H47). % 4.69/4.89 exact (zenon_H135 zenon_H71). % 4.69/4.89 apply (zenon_L79_); trivial. % 4.69/4.89 (* end of lemma zenon_L239_ *) % 4.69/4.89 assert (zenon_L240_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e1))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> False). % 4.69/4.89 do 0 intro. intros zenon_H1d zenon_H1e zenon_H9d zenon_H7b zenon_H13c zenon_Hfd zenon_H54 zenon_H165 zenon_H37 zenon_H132 zenon_H103 zenon_H36 zenon_H195 zenon_H135 zenon_H82 zenon_Hb4 zenon_H100 zenon_H7c zenon_Hb9 zenon_H5b zenon_H118 zenon_H20 zenon_H21. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ]. % 4.69/4.89 exact (zenon_H1e zenon_H23). % 4.69/4.89 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ]. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H5a | zenon_intro zenon_H119 ]. % 4.69/4.89 exact (zenon_H5b zenon_H5a). % 4.69/4.89 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H9c | zenon_intro zenon_H11c ]. % 4.69/4.89 apply (zenon_L92_); trivial. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H87 ]. % 4.69/4.89 apply (zenon_L88_); trivial. % 4.69/4.89 apply (zenon_L239_); trivial. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H24); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 4.69/4.89 exact (zenon_H20 zenon_H27). % 4.69/4.89 exact (zenon_H21 zenon_H26). % 4.69/4.89 (* end of lemma zenon_L240_ *) % 4.69/4.89 assert (zenon_L241_ : ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (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 (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 4.69/4.89 do 0 intro. intros zenon_H171 zenon_H11f zenon_H1e zenon_H118 zenon_Hb4 zenon_H82 zenon_H195 zenon_H165 zenon_H37 zenon_H9d zenon_H54 zenon_Hfd zenon_H13c zenon_H103 zenon_H100 zenon_H7c zenon_H36 zenon_H132 zenon_H7b zenon_Hb9 zenon_H5b zenon_H20 zenon_H21 zenon_H1d. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H135 | zenon_intro zenon_H104 ]. % 4.69/4.89 apply (zenon_L240_); trivial. % 4.69/4.89 apply (zenon_L73_); trivial. % 4.69/4.89 (* end of lemma zenon_L241_ *) % 4.69/4.89 assert (zenon_L242_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 4.69/4.89 do 0 intro. intros zenon_H114 zenon_H1e zenon_H9d zenon_H95 zenon_H82 zenon_Hb4 zenon_Hb3 zenon_H100 zenon_H85 zenon_H4c zenon_Hd0 zenon_H94 zenon_Hdf zenon_H135 zenon_H13e zenon_H7c zenon_H5b zenon_H137 zenon_H70 zenon_H132 zenon_H27 zenon_Hc3 zenon_H1ab zenon_He9 zenon_H75 zenon_H113 zenon_H140 zenon_H76 zenon_H2c. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H114); [ zenon_intro zenon_H23 | zenon_intro zenon_H115 ]. % 4.69/4.89 exact (zenon_H1e zenon_H23). % 4.69/4.89 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H34 | zenon_intro zenon_H116 ]. % 4.69/4.89 apply (zenon_L99_); trivial. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H42 | zenon_intro zenon_Hbd ]. % 4.69/4.89 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H34 | zenon_intro zenon_Hea ]. % 4.69/4.89 apply (zenon_L179_); trivial. % 4.69/4.89 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H3a | zenon_intro zenon_Heb ]. % 4.69/4.89 exact (zenon_Hc3 zenon_H3a). % 4.69/4.89 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_He5 | zenon_intro zenon_H7a ]. % 4.69/4.89 apply (zenon_L117_); trivial. % 4.69/4.89 apply (zenon_L101_); trivial. % 4.69/4.89 apply (zenon_L107_); trivial. % 4.69/4.89 (* end of lemma zenon_L242_ *) % 4.69/4.89 assert (zenon_L243_ : ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (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) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 4.69/4.89 do 0 intro. intros zenon_H153 zenon_H11f zenon_H1e zenon_H118 zenon_Hb4 zenon_H94 zenon_H85 zenon_H4c zenon_Hd0 zenon_H95 zenon_H103 zenon_H13c zenon_Hfd zenon_H54 zenon_H9d zenon_H76 zenon_H12e zenon_H100 zenon_H7c zenon_H36 zenon_H132 zenon_H135 zenon_H7b zenon_Hb9 zenon_H5b zenon_H114 zenon_H113 zenon_H1ab zenon_Hc3 zenon_H75 zenon_H70 zenon_He9 zenon_H13e zenon_H140 zenon_Hdf zenon_H82 zenon_Hb3 zenon_H137 zenon_H21 zenon_H1d. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H2c | zenon_intro zenon_H104 ]. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ]. % 4.69/4.89 exact (zenon_H1e zenon_H23). % 4.69/4.89 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ]. % 4.69/4.89 apply (zenon_L96_); trivial. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H24); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 4.69/4.89 apply (zenon_L242_); trivial. % 4.69/4.89 exact (zenon_H21 zenon_H26). % 4.69/4.89 apply (zenon_L73_); trivial. % 4.69/4.89 (* end of lemma zenon_L243_ *) % 4.69/4.89 assert (zenon_L244_ : (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (e1)) = (e0)) -> False). % 4.69/4.89 do 0 intro. intros zenon_Hd0 zenon_H25 zenon_H1a1. % 4.69/4.89 cut (((op (e0) (e1)) = (e0)) = ((op (e0) (e1)) = (op (e2) (e1)))). % 4.69/4.89 intro zenon_D_pnotp. % 4.69/4.89 apply zenon_Hd0. % 4.69/4.89 rewrite <- zenon_D_pnotp. % 4.69/4.89 exact zenon_H25. % 4.69/4.89 cut (((e0) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1c6]. % 4.69/4.89 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hd3]. % 4.69/4.89 congruence. % 4.69/4.89 apply zenon_Hd3. apply refl_equal. % 4.69/4.89 apply zenon_H1c6. apply sym_equal. exact zenon_H1a1. % 4.69/4.89 (* end of lemma zenon_L244_ *) % 4.69/4.89 assert (zenon_L245_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> False). % 4.69/4.89 do 0 intro. intros zenon_H12e zenon_H9d zenon_H87 zenon_Ha1 zenon_Hd7 zenon_H85 zenon_H76. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H8a | zenon_intro zenon_H12f ]. % 4.69/4.89 apply (zenon_L79_); trivial. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H130 ]. % 4.69/4.89 apply (zenon_L43_); trivial. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H81 | zenon_intro zenon_H79 ]. % 4.69/4.89 exact (zenon_H85 zenon_H81). % 4.69/4.89 exact (zenon_H76 zenon_H79). % 4.69/4.89 (* end of lemma zenon_L245_ *) % 4.69/4.89 assert (zenon_L246_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 4.69/4.89 do 0 intro. intros zenon_Hb3 zenon_Hb4 zenon_H76 zenon_H85 zenon_Hd7 zenon_H87 zenon_H12e zenon_H95 zenon_H123 zenon_H9d. % 4.69/4.89 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hb5 ]. % 4.69/4.89 exact (zenon_Hb4 zenon_Hb6). % 4.69/4.89 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hb7 ]. % 4.69/4.89 apply (zenon_L245_); trivial. % 4.69/4.89 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H98 | zenon_intro zenon_Hb0 ]. % 4.69/4.89 exact (zenon_H95 zenon_H98). % 4.69/4.89 apply (zenon_L77_); trivial. % 4.69/4.89 (* end of lemma zenon_L246_ *) % 4.69/4.89 assert (zenon_L247_ : ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 4.69/4.89 do 0 intro. intros zenon_H153 zenon_H11f zenon_H1e zenon_H118 zenon_H1c7 zenon_H142 zenon_H140 zenon_H76 zenon_H75 zenon_H179 zenon_Hd0 zenon_Hb3 zenon_H95 zenon_H9d zenon_Hd7 zenon_H85 zenon_H12e zenon_Hb4 zenon_H137 zenon_H7c zenon_H36 zenon_H132 zenon_H135 zenon_H7b zenon_Hb9 zenon_H5b zenon_H114 zenon_H113 zenon_H1ab zenon_Hc3 zenon_H70 zenon_He9 zenon_H100 zenon_H13e zenon_Hdf zenon_H82 zenon_H4c zenon_H94 zenon_H21 zenon_H1d. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H2c | zenon_intro zenon_H104 ]. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ]. % 4.69/4.89 exact (zenon_H1e zenon_H23). % 4.69/4.89 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ]. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H5a | zenon_intro zenon_H119 ]. % 4.69/4.89 exact (zenon_H5b zenon_H5a). % 4.69/4.89 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H9c | zenon_intro zenon_H11c ]. % 4.69/4.89 apply (zenon_L92_); trivial. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H87 ]. % 4.69/4.89 apply (zenon_L88_); trivial. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_H5a | zenon_intro zenon_H138 ]. % 4.69/4.89 exact (zenon_H5b zenon_H5a). % 4.69/4.89 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_H7e | zenon_intro zenon_H139 ]. % 4.69/4.89 exact (zenon_H7c zenon_H7e). % 4.69/4.89 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H123 ]. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H42 | zenon_intro zenon_H1c8 ]. % 4.69/4.89 apply (zenon_L100_); trivial. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H1c9 ]. % 4.69/4.89 apply (zenon_L244_); trivial. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H43 | zenon_intro zenon_H80 ]. % 4.69/4.89 exact (zenon_H179 zenon_H43). % 4.69/4.89 apply (zenon_L103_); trivial. % 4.69/4.89 apply (zenon_L246_); trivial. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H24); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 4.69/4.89 apply (zenon_L242_); trivial. % 4.69/4.89 exact (zenon_H21 zenon_H26). % 4.69/4.89 apply (zenon_L73_); trivial. % 4.69/4.89 (* end of lemma zenon_L247_ *) % 4.69/4.89 assert (zenon_L248_ : ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> False). % 4.69/4.89 do 0 intro. intros zenon_H170 zenon_H153 zenon_H11f zenon_H1e zenon_H118 zenon_H1c7 zenon_H142 zenon_H140 zenon_H76 zenon_H75 zenon_H179 zenon_Hd0 zenon_Hb3 zenon_H9d zenon_Hd7 zenon_H12e zenon_Hb4 zenon_H137 zenon_H7c zenon_H36 zenon_H132 zenon_H135 zenon_H7b zenon_Hb9 zenon_H5b zenon_H114 zenon_H113 zenon_H1ab zenon_Hc3 zenon_H70 zenon_He9 zenon_H100 zenon_H13e zenon_Hdf zenon_H82 zenon_H4c zenon_H94 zenon_H21 zenon_H1d zenon_H152. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H95 | zenon_intro zenon_H145 ]. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H85 | zenon_intro zenon_H104 ]. % 4.69/4.89 apply (zenon_L247_); trivial. % 4.69/4.89 apply (zenon_L73_); trivial. % 4.69/4.89 apply (zenon_L130_); trivial. % 4.69/4.89 (* end of lemma zenon_L248_ *) % 4.69/4.89 assert (zenon_L249_ : ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (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) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> False). % 4.69/4.89 do 0 intro. intros zenon_H1ca zenon_Hd7 zenon_H142 zenon_H1c7 zenon_H170 zenon_H153 zenon_H11f zenon_H1e zenon_H118 zenon_Hb4 zenon_H94 zenon_H4c zenon_Hd0 zenon_H103 zenon_H13c zenon_Hfd zenon_H54 zenon_H9d zenon_H76 zenon_H12e zenon_H100 zenon_H7c zenon_H36 zenon_H132 zenon_H135 zenon_H7b zenon_Hb9 zenon_H5b zenon_H114 zenon_H113 zenon_H1ab zenon_Hc3 zenon_H75 zenon_H70 zenon_He9 zenon_H13e zenon_H140 zenon_Hdf zenon_H82 zenon_Hb3 zenon_H137 zenon_H21 zenon_H1d zenon_H152. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H95 | zenon_intro zenon_H179 ]. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H85 | zenon_intro zenon_H104 ]. % 4.69/4.89 apply (zenon_L243_); trivial. % 4.69/4.89 apply (zenon_L73_); trivial. % 4.69/4.89 apply (zenon_L248_); trivial. % 4.69/4.89 (* end of lemma zenon_L249_ *) % 4.69/4.89 assert (zenon_L250_ : ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (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 (e0) (e3)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((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)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> False). % 4.69/4.89 do 0 intro. intros zenon_H171 zenon_H152 zenon_H1d zenon_H137 zenon_Hb3 zenon_H82 zenon_Hdf zenon_H140 zenon_H13e zenon_H117 zenon_H142 zenon_H70 zenon_H75 zenon_H21 zenon_H113 zenon_H114 zenon_H5b zenon_Hb9 zenon_H7b zenon_H132 zenon_H36 zenon_H7c zenon_H100 zenon_H12e zenon_H76 zenon_H9d zenon_H54 zenon_Hfd zenon_H13c zenon_H103 zenon_Hd0 zenon_H4c zenon_H94 zenon_Hb4 zenon_H118 zenon_H1e zenon_H11f zenon_H153 zenon_H1ca zenon_Hd7 zenon_H1c7 zenon_H170 zenon_H1ab zenon_He9 zenon_H172. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H135 | zenon_intro zenon_H104 ]. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H95 | zenon_intro zenon_Hc3 ]. % 4.69/4.89 apply (zenon_L108_); trivial. % 4.69/4.89 apply (zenon_L249_); trivial. % 4.69/4.89 apply (zenon_L73_); trivial. % 4.69/4.89 (* end of lemma zenon_L250_ *) % 4.69/4.89 assert (zenon_L251_ : (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e3) (e3)) = (e2)) -> False). % 4.69/4.89 do 0 intro. intros zenon_H6c zenon_H8a zenon_H79. % 4.69/4.89 cut (((op (e0) (e3)) = (e2)) = ((op (e0) (e3)) = (op (e3) (e3)))). % 4.69/4.89 intro zenon_D_pnotp. % 4.69/4.89 apply zenon_H6c. % 4.69/4.89 rewrite <- zenon_D_pnotp. % 4.69/4.89 exact zenon_H8a. % 4.69/4.89 cut (((e2) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1aa]. % 4.69/4.89 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 4.69/4.89 congruence. % 4.69/4.89 apply zenon_H6f. apply refl_equal. % 4.69/4.89 apply zenon_H1aa. apply sym_equal. exact zenon_H79. % 4.69/4.89 (* end of lemma zenon_L251_ *) % 4.69/4.89 assert (zenon_L252_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 4.69/4.89 do 0 intro. intros zenon_H75 zenon_H145 zenon_H140 zenon_H8a zenon_H6c zenon_H2c. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H75); [ zenon_intro zenon_H6d | zenon_intro zenon_H77 ]. % 4.69/4.89 exact (zenon_H145 zenon_H6d). % 4.69/4.89 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H72 | zenon_intro zenon_H78 ]. % 4.69/4.89 exact (zenon_H140 zenon_H72). % 4.69/4.89 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H79 | zenon_intro zenon_H31 ]. % 4.69/4.89 apply (zenon_L251_); trivial. % 4.69/4.89 exact (zenon_H2c zenon_H31). % 4.69/4.89 (* end of lemma zenon_L252_ *) % 4.69/4.89 assert (zenon_L253_ : (((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)) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 4.69/4.89 do 0 intro. intros zenon_H100 zenon_Hb4 zenon_H82 zenon_H25 zenon_H9d zenon_Hb8 zenon_H75 zenon_H145 zenon_H140 zenon_H6c zenon_H2c. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hb6 | zenon_intro zenon_H105 ]. % 4.69/4.89 exact (zenon_Hb4 zenon_Hb6). % 4.69/4.89 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H5e | zenon_intro zenon_H106 ]. % 4.69/4.89 apply (zenon_L148_); trivial. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_H92 | zenon_intro zenon_H8a ]. % 4.69/4.89 apply (zenon_L149_); trivial. % 4.69/4.89 apply (zenon_L252_); trivial. % 4.69/4.89 (* end of lemma zenon_L253_ *) % 4.69/4.89 assert (zenon_L254_ : ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 4.69/4.89 do 0 intro. intros zenon_H153 zenon_H11f zenon_H1e zenon_H118 zenon_H7b zenon_H135 zenon_H195 zenon_H36 zenon_H165 zenon_H132 zenon_H37 zenon_H54 zenon_Hfd zenon_H13c zenon_H103 zenon_Hb4 zenon_H82 zenon_H9d zenon_H75 zenon_H6c zenon_H140 zenon_H145 zenon_H100 zenon_Hb9 zenon_H5b zenon_H20 zenon_H21 zenon_H1d. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H2c | zenon_intro zenon_H104 ]. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ]. % 4.69/4.89 exact (zenon_H1e zenon_H23). % 4.69/4.89 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ]. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H5a | zenon_intro zenon_H119 ]. % 4.69/4.89 exact (zenon_H5b zenon_H5a). % 4.69/4.89 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H9c | zenon_intro zenon_H11c ]. % 4.69/4.89 apply (zenon_L92_); trivial. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H87 ]. % 4.69/4.89 apply (zenon_L253_); trivial. % 4.69/4.89 apply (zenon_L239_); trivial. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H24); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 4.69/4.89 exact (zenon_H20 zenon_H27). % 4.69/4.89 exact (zenon_H21 zenon_H26). % 4.69/4.89 apply (zenon_L73_); trivial. % 4.69/4.89 (* end of lemma zenon_L254_ *) % 4.69/4.89 assert (zenon_L255_ : ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> False). % 4.69/4.89 do 0 intro. intros zenon_H1cb zenon_H153 zenon_H11f zenon_H1e zenon_H118 zenon_H7b zenon_H36 zenon_H165 zenon_H132 zenon_H37 zenon_H54 zenon_Hfd zenon_H13c zenon_H103 zenon_Hb4 zenon_H82 zenon_H9d zenon_H75 zenon_H6c zenon_H140 zenon_H145 zenon_H100 zenon_Hb9 zenon_H5b zenon_H20 zenon_H21 zenon_H1d zenon_H171. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H195 | zenon_intro zenon_H76 ]. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H135 | zenon_intro zenon_H104 ]. % 4.69/4.89 apply (zenon_L254_); trivial. % 4.69/4.89 apply (zenon_L73_); trivial. % 4.69/4.89 apply (zenon_L130_); trivial. % 4.69/4.89 (* end of lemma zenon_L255_ *) % 4.69/4.89 assert (zenon_L256_ : ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (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 (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (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 (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> False). % 4.69/4.89 do 0 intro. intros zenon_H173 zenon_H6c zenon_H171 zenon_H11f zenon_H1e zenon_H118 zenon_Hb4 zenon_H82 zenon_H165 zenon_H37 zenon_H9d zenon_H54 zenon_Hfd zenon_H13c zenon_H103 zenon_H100 zenon_H36 zenon_H132 zenon_H7b zenon_Hb9 zenon_H5b zenon_H20 zenon_H21 zenon_H1d zenon_H152 zenon_H137 zenon_Hb3 zenon_Hdf zenon_H140 zenon_H13e zenon_H117 zenon_H142 zenon_H70 zenon_H75 zenon_H113 zenon_H114 zenon_H12e zenon_Hd0 zenon_H4c zenon_H94 zenon_H153 zenon_H1ca zenon_Hd7 zenon_H1c7 zenon_H170 zenon_H1ab zenon_He9 zenon_H172 zenon_H1cb. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H7c | zenon_intro zenon_H145 ]. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H195 | zenon_intro zenon_H76 ]. % 4.69/4.89 apply (zenon_L241_); trivial. % 4.69/4.89 apply (zenon_L250_); trivial. % 4.69/4.89 apply (zenon_L255_); trivial. % 4.69/4.89 (* end of lemma zenon_L256_ *) % 4.69/4.89 assert (zenon_L257_ : ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (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)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((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)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> False). % 4.69/4.89 do 0 intro. intros zenon_H1cc zenon_H1cb zenon_H172 zenon_He9 zenon_H1ab zenon_H170 zenon_H1c7 zenon_Hd7 zenon_H1ca zenon_H153 zenon_H94 zenon_Hd0 zenon_H12e zenon_H114 zenon_H113 zenon_H75 zenon_H70 zenon_H142 zenon_H117 zenon_H13e zenon_H140 zenon_Hdf zenon_Hb3 zenon_H137 zenon_H152 zenon_H6c zenon_H173 zenon_H1d zenon_H21 zenon_H20 zenon_H5b zenon_Hb9 zenon_H7b zenon_H132 zenon_H36 zenon_H7c zenon_H100 zenon_H103 zenon_H13c zenon_Hfd zenon_H54 zenon_H9d zenon_H37 zenon_H165 zenon_H82 zenon_Hb4 zenon_H118 zenon_H1e zenon_H11f zenon_H171. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H195 | zenon_intro zenon_H4c ]. % 4.69/4.89 apply (zenon_L241_); trivial. % 4.69/4.89 apply (zenon_L256_); trivial. % 4.69/4.89 (* end of lemma zenon_L257_ *) % 4.69/4.89 assert (zenon_L258_ : ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (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 (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (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 (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> False). % 4.69/4.89 do 0 intro. intros zenon_H171 zenon_H11f zenon_H1e zenon_H118 zenon_Hb4 zenon_H82 zenon_H165 zenon_H37 zenon_H9d zenon_H54 zenon_Hfd zenon_H13c zenon_H103 zenon_H100 zenon_H36 zenon_H132 zenon_H7b zenon_Hb9 zenon_H5b zenon_H20 zenon_H21 zenon_H1d zenon_H173 zenon_H6c zenon_H152 zenon_H137 zenon_Hb3 zenon_Hdf zenon_H140 zenon_H13e zenon_H117 zenon_H142 zenon_H70 zenon_H75 zenon_H113 zenon_H114 zenon_H12e zenon_Hd0 zenon_H94 zenon_H153 zenon_H1ca zenon_Hd7 zenon_H1c7 zenon_H170 zenon_H1ab zenon_He9 zenon_H172 zenon_H1cb zenon_H1cc. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H7c | zenon_intro zenon_H145 ]. % 4.69/4.89 apply (zenon_L257_); trivial. % 4.69/4.89 apply (zenon_L255_); trivial. % 4.69/4.89 (* end of lemma zenon_L258_ *) % 4.69/4.89 assert (zenon_L259_ : ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> False). % 4.69/4.89 do 0 intro. intros zenon_H11e zenon_H1cc zenon_H1cb zenon_H172 zenon_He9 zenon_H1ab zenon_H170 zenon_H1c7 zenon_Hd7 zenon_H1ca zenon_H94 zenon_Hd0 zenon_H75 zenon_H70 zenon_H142 zenon_H117 zenon_H152 zenon_H6c zenon_H173 zenon_H165 zenon_H171 zenon_H1d zenon_H21 zenon_H20 zenon_H118 zenon_H100 zenon_H13e zenon_H140 zenon_Hdf zenon_H95 zenon_H103 zenon_H13c zenon_Hfd zenon_H54 zenon_H9d zenon_H85 zenon_H113 zenon_H12e zenon_Hb3 zenon_H82 zenon_Hb4 zenon_H137 zenon_H7c zenon_H36 zenon_H132 zenon_H135 zenon_H7b zenon_Hb9 zenon_H5b zenon_H195 zenon_Hef zenon_H28 zenon_H101 zenon_H114 zenon_H1e zenon_H11f zenon_H153. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H2b | zenon_intro zenon_H37 ]. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H2c | zenon_intro zenon_H104 ]. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ]. % 4.69/4.89 exact (zenon_H1e zenon_H23). % 4.69/4.89 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ]. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H114); [ zenon_intro zenon_H23 | zenon_intro zenon_H115 ]. % 4.69/4.89 exact (zenon_H1e zenon_H23). % 4.69/4.89 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H34 | zenon_intro zenon_H116 ]. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H5a | zenon_intro zenon_H119 ]. % 4.69/4.89 exact (zenon_H5b zenon_H5a). % 4.69/4.89 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H9c | zenon_intro zenon_H11c ]. % 4.69/4.89 apply (zenon_L92_); trivial. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H87 ]. % 4.69/4.89 apply (zenon_L88_); trivial. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_H5a | zenon_intro zenon_H138 ]. % 4.69/4.89 exact (zenon_H5b zenon_H5a). % 4.69/4.89 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_H7e | zenon_intro zenon_H139 ]. % 4.69/4.89 exact (zenon_H7c zenon_H7e). % 4.69/4.89 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H123 ]. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hb6 | zenon_intro zenon_H105 ]. % 4.69/4.89 exact (zenon_Hb4 zenon_Hb6). % 4.69/4.89 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H5e | zenon_intro zenon_H106 ]. % 4.69/4.89 apply (zenon_L148_); trivial. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_H92 | zenon_intro zenon_H8a ]. % 4.69/4.89 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hb5 ]. % 4.69/4.89 exact (zenon_Hb4 zenon_Hb6). % 4.69/4.89 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hb7 ]. % 4.69/4.89 apply (zenon_L52_); trivial. % 4.69/4.89 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H98 | zenon_intro zenon_Hb0 ]. % 4.69/4.89 exact (zenon_H95 zenon_H98). % 4.69/4.89 apply (zenon_L231_); trivial. % 4.69/4.89 apply (zenon_L98_); trivial. % 4.69/4.89 apply (zenon_L78_); trivial. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H42 | zenon_intro zenon_Hbd ]. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_H5a | zenon_intro zenon_H138 ]. % 4.69/4.89 exact (zenon_H5b zenon_H5a). % 4.69/4.89 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_H7e | zenon_intro zenon_H139 ]. % 4.69/4.89 exact (zenon_H7c zenon_H7e). % 4.69/4.89 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H123 ]. % 4.69/4.89 apply (zenon_L100_); trivial. % 4.69/4.89 apply (zenon_L233_); trivial. % 4.69/4.89 apply (zenon_L236_); trivial. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H24); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 4.69/4.89 exact (zenon_H20 zenon_H27). % 4.69/4.89 exact (zenon_H21 zenon_H26). % 4.69/4.89 apply (zenon_L73_); trivial. % 4.69/4.89 apply (zenon_L258_); trivial. % 4.69/4.89 (* end of lemma zenon_L259_ *) % 4.69/4.89 assert (zenon_L260_ : ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (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 (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> False). % 4.69/4.89 do 0 intro. intros zenon_H19a zenon_H153 zenon_H11f zenon_H114 zenon_Hb3 zenon_H12e zenon_H113 zenon_H85 zenon_H95 zenon_Hdf zenon_H140 zenon_H13e zenon_H171 zenon_H165 zenon_H173 zenon_H6c zenon_H152 zenon_H117 zenon_H142 zenon_H70 zenon_H75 zenon_Hd0 zenon_H94 zenon_H1ca zenon_Hd7 zenon_H1c7 zenon_H170 zenon_H1ab zenon_He9 zenon_H172 zenon_H1cb zenon_H1cc zenon_H11e zenon_H1d zenon_H21 zenon_H20 zenon_H5b zenon_Hb9 zenon_H7b zenon_H135 zenon_H132 zenon_H36 zenon_H7c zenon_H137 zenon_H104 zenon_H198 zenon_H194 zenon_Hf6 zenon_H16c zenon_H195 zenon_H103 zenon_Hef zenon_H28 zenon_H13c zenon_H29 zenon_H101 zenon_H118 zenon_H1e zenon_H1c4 zenon_H186 zenon_H4c zenon_H4b zenon_H100 zenon_H54 zenon_Hfd zenon_H9d zenon_H82 zenon_H18f zenon_H1c5. % 4.69/4.89 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H2b | zenon_intro zenon_Hb4 ]. % 4.69/4.89 apply (zenon_L229_); trivial. % 4.69/4.89 apply (zenon_L259_); trivial. % 4.69/4.89 (* end of lemma zenon_L260_ *) % 4.69/4.89 assert (zenon_L261_ : (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> False). % 4.69/4.89 do 0 intro. intros zenon_H198 zenon_H25 zenon_H10e. % 4.69/4.89 cut (((op (e0) (e1)) = (e0)) = ((op (e0) (e1)) = (op (e3) (e1)))). % 4.69/4.89 intro zenon_D_pnotp. % 4.69/4.89 apply zenon_H198. % 4.69/4.89 rewrite <- zenon_D_pnotp. % 4.69/4.89 exact zenon_H25. % 4.69/4.89 cut (((e0) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H10f]. % 4.69/4.89 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hd3]. % 4.69/4.89 congruence. % 4.69/4.89 apply zenon_Hd3. apply refl_equal. % 4.69/4.89 apply zenon_H10f. apply sym_equal. exact zenon_H10e. % 4.69/4.89 (* end of lemma zenon_L261_ *) % 4.69/4.89 assert (zenon_L262_ : (~((op (e3) (op (e3) (e3))) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e2)) -> False). % 4.69/4.89 do 0 intro. intros zenon_H1cd zenon_H79. % 4.69/4.89 cut (((op (e3) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H76]. % 4.69/4.89 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H56]. % 4.69/4.89 congruence. % 4.69/4.89 apply zenon_H56. apply refl_equal. % 4.69/4.89 exact (zenon_H76 zenon_H79). % 4.69/4.89 (* end of lemma zenon_L262_ *) % 4.69/4.89 assert (zenon_L263_ : (~((op (op (e3) (op (e3) (e3))) (op (e3) (e3))) = (op (e0) (e2)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e3) (e2)) = (e0)) -> False). % 4.69/4.89 do 0 intro. intros zenon_H1ce zenon_H79 zenon_Hf7. % 4.69/4.89 cut (((op (e3) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H76]. % 4.69/4.89 cut (((op (e3) (op (e3) (e3))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1cf]. % 4.69/4.89 congruence. % 4.69/4.89 cut (((op (e3) (e2)) = (e0)) = ((op (e3) (op (e3) (e3))) = (e0))). % 4.69/4.89 intro zenon_D_pnotp. % 4.69/4.89 apply zenon_H1cf. % 4.69/4.89 rewrite <- zenon_D_pnotp. % 4.69/4.89 exact zenon_Hf7. % 4.69/4.89 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 4.69/4.89 cut (((op (e3) (e2)) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H1d0]. % 4.69/4.89 congruence. % 4.69/4.89 elim (classic ((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 4.69/4.89 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3)))) = ((op (e3) (e2)) = (op (e3) (op (e3) (e3))))). % 4.69/4.89 intro zenon_D_pnotp. % 4.69/4.89 apply zenon_H1d0. % 4.69/4.89 rewrite <- zenon_D_pnotp. % 4.69/4.89 exact zenon_H149. % 4.69/4.89 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H14a]. % 4.69/4.89 cut (((op (e3) (op (e3) (e3))) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1cd]. % 4.69/4.89 congruence. % 4.69/4.89 apply (zenon_L262_); trivial. % 4.69/4.89 apply zenon_H14a. apply refl_equal. % 4.69/4.89 apply zenon_H14a. apply refl_equal. % 4.69/4.89 apply zenon_H52. apply refl_equal. % 4.69/4.89 exact (zenon_H76 zenon_H79). % 4.69/4.89 (* end of lemma zenon_L263_ *) % 4.69/4.89 assert (zenon_L264_ : ((op (e0) (e2)) = (e1)) -> ((op (e3) (e2)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> False). % 4.69/4.89 do 0 intro. intros zenon_Hb8 zenon_Hf7 zenon_H79. % 4.69/4.89 apply (zenon_notand_s _ _ ax8); [ zenon_intro zenon_H1d2 | zenon_intro zenon_H1d1 ]. % 4.69/4.89 elim (classic ((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 4.69/4.89 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3)))) = ((e0) = (op (e3) (op (e3) (e3))))). % 4.69/4.89 intro zenon_D_pnotp. % 4.69/4.89 apply zenon_H1d2. % 4.69/4.89 rewrite <- zenon_D_pnotp. % 4.69/4.89 exact zenon_H149. % 4.69/4.89 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H14a]. % 4.69/4.89 cut (((op (e3) (op (e3) (e3))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1cf]. % 4.69/4.89 congruence. % 4.69/4.89 cut (((op (e3) (e2)) = (e0)) = ((op (e3) (op (e3) (e3))) = (e0))). % 4.69/4.89 intro zenon_D_pnotp. % 4.69/4.89 apply zenon_H1cf. % 4.69/4.89 rewrite <- zenon_D_pnotp. % 4.69/4.89 exact zenon_Hf7. % 4.69/4.89 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 4.69/4.89 cut (((op (e3) (e2)) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H1d0]. % 4.69/4.89 congruence. % 4.69/4.89 elim (classic ((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 4.69/4.89 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3)))) = ((op (e3) (e2)) = (op (e3) (op (e3) (e3))))). % 4.69/4.89 intro zenon_D_pnotp. % 4.69/4.89 apply zenon_H1d0. % 4.69/4.89 rewrite <- zenon_D_pnotp. % 4.69/4.89 exact zenon_H149. % 4.69/4.89 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H14a]. % 4.69/4.89 cut (((op (e3) (op (e3) (e3))) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1cd]. % 4.69/4.89 congruence. % 4.69/4.89 apply (zenon_L262_); trivial. % 4.69/4.89 apply zenon_H14a. apply refl_equal. % 4.69/4.89 apply zenon_H14a. apply refl_equal. % 4.69/4.89 apply zenon_H52. apply refl_equal. % 4.69/4.89 apply zenon_H14a. apply refl_equal. % 4.69/4.89 apply zenon_H14a. apply refl_equal. % 4.69/4.89 apply (zenon_notand_s _ _ zenon_H1d1); [ zenon_intro zenon_H1aa | zenon_intro zenon_H1d3 ]. % 4.69/4.89 apply zenon_H1aa. apply sym_equal. exact zenon_H79. % 4.69/4.89 elim (classic ((op (op (e3) (op (e3) (e3))) (op (e3) (e3))) = (op (op (e3) (op (e3) (e3))) (op (e3) (e3))))); [ zenon_intro zenon_H14e | zenon_intro zenon_H14f ]. % 4.69/4.89 cut (((op (op (e3) (op (e3) (e3))) (op (e3) (e3))) = (op (op (e3) (op (e3) (e3))) (op (e3) (e3)))) = ((e1) = (op (op (e3) (op (e3) (e3))) (op (e3) (e3))))). % 4.69/4.89 intro zenon_D_pnotp. % 4.69/4.89 apply zenon_H1d3. % 4.69/4.89 rewrite <- zenon_D_pnotp. % 4.69/4.89 exact zenon_H14e. % 4.69/4.89 cut (((op (op (e3) (op (e3) (e3))) (op (e3) (e3))) = (op (op (e3) (op (e3) (e3))) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H14f]. % 4.69/4.89 cut (((op (op (e3) (op (e3) (e3))) (op (e3) (e3))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d4]. % 4.69/4.89 congruence. % 4.69/4.89 cut (((op (e0) (e2)) = (e1)) = ((op (op (e3) (op (e3) (e3))) (op (e3) (e3))) = (e1))). % 4.69/4.89 intro zenon_D_pnotp. % 4.69/4.89 apply zenon_H1d4. % 4.69/4.89 rewrite <- zenon_D_pnotp. % 4.69/4.89 exact zenon_Hb8. % 4.69/4.89 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 4.69/4.89 cut (((op (e0) (e2)) = (op (op (e3) (op (e3) (e3))) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H1d5]. % 4.69/4.89 congruence. % 4.69/4.89 elim (classic ((op (op (e3) (op (e3) (e3))) (op (e3) (e3))) = (op (op (e3) (op (e3) (e3))) (op (e3) (e3))))); [ zenon_intro zenon_H14e | zenon_intro zenon_H14f ]. % 4.69/4.89 cut (((op (op (e3) (op (e3) (e3))) (op (e3) (e3))) = (op (op (e3) (op (e3) (e3))) (op (e3) (e3)))) = ((op (e0) (e2)) = (op (op (e3) (op (e3) (e3))) (op (e3) (e3))))). % 4.69/4.89 intro zenon_D_pnotp. % 4.69/4.89 apply zenon_H1d5. % 4.69/4.89 rewrite <- zenon_D_pnotp. % 4.69/4.89 exact zenon_H14e. % 4.69/4.89 cut (((op (op (e3) (op (e3) (e3))) (op (e3) (e3))) = (op (op (e3) (op (e3) (e3))) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H14f]. % 4.69/4.89 cut (((op (op (e3) (op (e3) (e3))) (op (e3) (e3))) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1ce]. % 4.69/4.89 congruence. % 4.69/4.89 apply (zenon_L263_); trivial. % 4.69/4.89 apply zenon_H14f. apply refl_equal. % 4.69/4.89 apply zenon_H14f. apply refl_equal. % 4.69/4.89 apply zenon_H9b. apply refl_equal. % 4.69/4.89 apply zenon_H14f. apply refl_equal. % 4.69/4.89 apply zenon_H14f. apply refl_equal. % 4.69/4.89 (* end of lemma zenon_L264_ *) % 4.69/4.89 assert (zenon_L265_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e3) (e2)) = (e0)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e3) (e3)) = (e3))) -> False). % 4.69/4.90 do 0 intro. intros zenon_H75 zenon_H145 zenon_H140 zenon_Hf7 zenon_Hb8 zenon_H2c. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H75); [ zenon_intro zenon_H6d | zenon_intro zenon_H77 ]. % 4.69/4.90 exact (zenon_H145 zenon_H6d). % 4.69/4.90 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H72 | zenon_intro zenon_H78 ]. % 4.69/4.90 exact (zenon_H140 zenon_H72). % 4.69/4.90 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H79 | zenon_intro zenon_H31 ]. % 4.69/4.90 apply (zenon_L264_); trivial. % 4.69/4.90 exact (zenon_H2c zenon_H31). % 4.69/4.90 (* end of lemma zenon_L265_ *) % 4.69/4.90 assert (zenon_L266_ : (~((op (e2) (op (e2) (e2))) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e3)) -> False). % 4.69/4.90 do 0 intro. intros zenon_H1d6 zenon_H50. % 4.69/4.90 cut (((op (e2) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 4.69/4.90 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 4.69/4.90 congruence. % 4.69/4.90 apply zenon_H5c. apply refl_equal. % 4.69/4.90 exact (zenon_H4d zenon_H50). % 4.69/4.90 (* end of lemma zenon_L266_ *) % 4.69/4.90 assert (zenon_L267_ : ((op (e0) (e3)) = (e1)) -> ((op (e2) (e3)) = (e0)) -> ((op (e2) (e2)) = (e3)) -> False). % 4.69/4.90 do 0 intro. intros zenon_H87 zenon_H80 zenon_H50. % 4.69/4.90 apply (zenon_notand_s _ _ ax10); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H1d7 ]. % 4.69/4.90 elim (classic ((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [ zenon_intro zenon_H17d | zenon_intro zenon_H17e ]. % 4.69/4.90 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2)))) = ((e0) = (op (e2) (op (e2) (e2))))). % 4.69/4.90 intro zenon_D_pnotp. % 4.69/4.90 apply zenon_H1a5. % 4.69/4.90 rewrite <- zenon_D_pnotp. % 4.69/4.90 exact zenon_H17d. % 4.69/4.90 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H17e]. % 4.69/4.90 cut (((op (e2) (op (e2) (e2))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1a2]. % 4.69/4.90 congruence. % 4.69/4.90 cut (((op (e2) (e3)) = (e0)) = ((op (e2) (op (e2) (e2))) = (e0))). % 4.69/4.90 intro zenon_D_pnotp. % 4.69/4.90 apply zenon_H1a2. % 4.69/4.90 rewrite <- zenon_D_pnotp. % 4.69/4.90 exact zenon_H80. % 4.69/4.90 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 4.69/4.90 cut (((op (e2) (e3)) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H1d8]. % 4.69/4.90 congruence. % 4.69/4.90 elim (classic ((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [ zenon_intro zenon_H17d | zenon_intro zenon_H17e ]. % 4.69/4.90 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2)))) = ((op (e2) (e3)) = (op (e2) (op (e2) (e2))))). % 4.69/4.90 intro zenon_D_pnotp. % 4.69/4.90 apply zenon_H1d8. % 4.69/4.90 rewrite <- zenon_D_pnotp. % 4.69/4.90 exact zenon_H17d. % 4.69/4.90 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H17e]. % 4.69/4.90 cut (((op (e2) (op (e2) (e2))) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1d6]. % 4.69/4.90 congruence. % 4.69/4.90 apply (zenon_L266_); trivial. % 4.69/4.90 apply zenon_H17e. apply refl_equal. % 4.69/4.90 apply zenon_H17e. apply refl_equal. % 4.69/4.90 apply zenon_H52. apply refl_equal. % 4.69/4.90 apply zenon_H17e. apply refl_equal. % 4.69/4.90 apply zenon_H17e. apply refl_equal. % 4.69/4.90 apply (zenon_notand_s _ _ zenon_H1d7); [ zenon_intro zenon_H1da | zenon_intro zenon_H1d9 ]. % 4.69/4.90 apply zenon_H1da. apply sym_equal. exact zenon_H50. % 4.69/4.90 elim (classic ((op (op (e2) (op (e2) (e2))) (op (e2) (e2))) = (op (op (e2) (op (e2) (e2))) (op (e2) (e2))))); [ zenon_intro zenon_H182 | zenon_intro zenon_H183 ]. % 4.69/4.90 cut (((op (op (e2) (op (e2) (e2))) (op (e2) (e2))) = (op (op (e2) (op (e2) (e2))) (op (e2) (e2)))) = ((e1) = (op (op (e2) (op (e2) (e2))) (op (e2) (e2))))). % 4.69/4.90 intro zenon_D_pnotp. % 4.69/4.90 apply zenon_H1d9. % 4.69/4.90 rewrite <- zenon_D_pnotp. % 4.69/4.90 exact zenon_H182. % 4.69/4.90 cut (((op (op (e2) (op (e2) (e2))) (op (e2) (e2))) = (op (op (e2) (op (e2) (e2))) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H183]. % 4.69/4.90 cut (((op (op (e2) (op (e2) (e2))) (op (e2) (e2))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1db]. % 4.69/4.90 congruence. % 4.69/4.90 cut (((op (e0) (e3)) = (e1)) = ((op (op (e2) (op (e2) (e2))) (op (e2) (e2))) = (e1))). % 4.69/4.90 intro zenon_D_pnotp. % 4.69/4.90 apply zenon_H1db. % 4.69/4.90 rewrite <- zenon_D_pnotp. % 4.69/4.90 exact zenon_H87. % 4.69/4.90 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 4.69/4.90 cut (((op (e0) (e3)) = (op (op (e2) (op (e2) (e2))) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H1dc]. % 4.69/4.90 congruence. % 4.69/4.90 elim (classic ((op (op (e2) (op (e2) (e2))) (op (e2) (e2))) = (op (op (e2) (op (e2) (e2))) (op (e2) (e2))))); [ zenon_intro zenon_H182 | zenon_intro zenon_H183 ]. % 4.69/4.90 cut (((op (op (e2) (op (e2) (e2))) (op (e2) (e2))) = (op (op (e2) (op (e2) (e2))) (op (e2) (e2)))) = ((op (e0) (e3)) = (op (op (e2) (op (e2) (e2))) (op (e2) (e2))))). % 4.69/4.90 intro zenon_D_pnotp. % 4.69/4.90 apply zenon_H1dc. % 4.69/4.90 rewrite <- zenon_D_pnotp. % 4.69/4.90 exact zenon_H182. % 4.69/4.90 cut (((op (op (e2) (op (e2) (e2))) (op (e2) (e2))) = (op (op (e2) (op (e2) (e2))) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H183]. % 4.69/4.90 cut (((op (op (e2) (op (e2) (e2))) (op (e2) (e2))) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1dd]. % 4.69/4.90 congruence. % 4.69/4.90 cut (((op (e2) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 4.69/4.90 cut (((op (e2) (op (e2) (e2))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1a2]. % 4.69/4.90 congruence. % 4.69/4.90 cut (((op (e2) (e3)) = (e0)) = ((op (e2) (op (e2) (e2))) = (e0))). % 4.69/4.90 intro zenon_D_pnotp. % 4.69/4.90 apply zenon_H1a2. % 4.69/4.90 rewrite <- zenon_D_pnotp. % 4.69/4.90 exact zenon_H80. % 4.69/4.90 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 4.69/4.90 cut (((op (e2) (e3)) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H1d8]. % 4.69/4.90 congruence. % 4.69/4.90 elim (classic ((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [ zenon_intro zenon_H17d | zenon_intro zenon_H17e ]. % 4.69/4.90 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2)))) = ((op (e2) (e3)) = (op (e2) (op (e2) (e2))))). % 4.69/4.90 intro zenon_D_pnotp. % 4.69/4.90 apply zenon_H1d8. % 4.69/4.90 rewrite <- zenon_D_pnotp. % 4.69/4.90 exact zenon_H17d. % 4.69/4.90 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H17e]. % 4.69/4.90 cut (((op (e2) (op (e2) (e2))) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1d6]. % 4.69/4.90 congruence. % 4.69/4.90 apply (zenon_L266_); trivial. % 4.69/4.90 apply zenon_H17e. apply refl_equal. % 4.69/4.90 apply zenon_H17e. apply refl_equal. % 4.69/4.90 apply zenon_H52. apply refl_equal. % 4.69/4.90 exact (zenon_H4d zenon_H50). % 4.69/4.90 apply zenon_H183. apply refl_equal. % 4.69/4.90 apply zenon_H183. apply refl_equal. % 4.69/4.90 apply zenon_H9b. apply refl_equal. % 4.69/4.90 apply zenon_H183. apply refl_equal. % 4.69/4.90 apply zenon_H183. apply refl_equal. % 4.69/4.90 (* end of lemma zenon_L267_ *) % 4.69/4.90 assert (zenon_L268_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e3)) = (e1)) -> ((op (e2) (e3)) = (e0)) -> False). % 4.69/4.90 do 0 intro. intros zenon_H4b zenon_H179 zenon_H16c zenon_H4c zenon_H87 zenon_H80. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H4b); [ zenon_intro zenon_H43 | zenon_intro zenon_H4e ]. % 4.69/4.90 exact (zenon_H179 zenon_H43). % 4.69/4.90 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H48 | zenon_intro zenon_H4f ]. % 4.69/4.90 exact (zenon_H16c zenon_H48). % 4.69/4.90 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H51 | zenon_intro zenon_H50 ]. % 4.69/4.90 exact (zenon_H4c zenon_H51). % 4.69/4.90 apply (zenon_L267_); trivial. % 4.69/4.90 (* end of lemma zenon_L268_ *) % 4.69/4.90 assert (zenon_L269_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e3)) = (e1)) -> False). % 4.69/4.90 do 0 intro. intros zenon_H1c7 zenon_H1ab zenon_H34 zenon_H25 zenon_Hd0 zenon_H4b zenon_H179 zenon_H16c zenon_H4c zenon_H87. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H42 | zenon_intro zenon_H1c8 ]. % 4.69/4.90 apply (zenon_L179_); trivial. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H1c9 ]. % 4.69/4.90 apply (zenon_L244_); trivial. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H43 | zenon_intro zenon_H80 ]. % 4.69/4.90 exact (zenon_H179 zenon_H43). % 4.69/4.90 apply (zenon_L268_); trivial. % 4.69/4.90 (* end of lemma zenon_L269_ *) % 4.69/4.90 assert (zenon_L270_ : ((op (e2) (e1)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> False). % 4.69/4.90 do 0 intro. intros zenon_Hf1 zenon_H9a zenon_H9d. % 4.69/4.90 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H83 | zenon_intro zenon_H5c ]. % 4.69/4.90 cut (((e2) = (e2)) = ((e1) = (e2))). % 4.69/4.90 intro zenon_D_pnotp. % 4.69/4.90 apply zenon_H9d. % 4.69/4.90 rewrite <- zenon_D_pnotp. % 4.69/4.90 exact zenon_H83. % 4.69/4.90 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 4.69/4.90 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9e]. % 4.69/4.90 congruence. % 4.69/4.90 cut (((op (e2) (e1)) = (e1)) = ((e2) = (e1))). % 4.69/4.90 intro zenon_D_pnotp. % 4.69/4.90 apply zenon_H9e. % 4.69/4.90 rewrite <- zenon_D_pnotp. % 4.69/4.90 exact zenon_Hf1. % 4.69/4.90 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 4.69/4.90 cut (((op (e2) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 4.69/4.90 congruence. % 4.69/4.90 exact (zenon_H96 zenon_H9a). % 4.69/4.90 apply zenon_H9b. apply refl_equal. % 4.69/4.90 apply zenon_H5c. apply refl_equal. % 4.69/4.90 apply zenon_H5c. apply refl_equal. % 4.69/4.90 (* end of lemma zenon_L270_ *) % 4.69/4.90 assert (zenon_L271_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> False). % 4.69/4.90 do 0 intro. intros zenon_H94 zenon_H82 zenon_H42 zenon_H9d zenon_Hf1 zenon_H4c zenon_H85. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H98 | zenon_intro zenon_H97 ]. % 4.69/4.90 apply (zenon_L31_); trivial. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H9a | zenon_intro zenon_H99 ]. % 4.69/4.90 apply (zenon_L270_); trivial. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H99); [ zenon_intro zenon_H51 | zenon_intro zenon_H81 ]. % 4.69/4.90 exact (zenon_H4c zenon_H51). % 4.69/4.90 exact (zenon_H85 zenon_H81). % 4.69/4.90 (* end of lemma zenon_L271_ *) % 4.69/4.90 assert (zenon_L272_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (e3))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 4.69/4.90 do 0 intro. intros zenon_H1de zenon_H2b zenon_Hfa zenon_H13c zenon_H54 zenon_H28 zenon_H25 zenon_H198 zenon_H2c zenon_Hb8 zenon_H140 zenon_H75 zenon_H145. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H1de); [ zenon_intro zenon_Hbd | zenon_intro zenon_H1df ]. % 4.69/4.90 apply (zenon_L234_); trivial. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_H10e | zenon_intro zenon_H1e0 ]. % 4.69/4.90 apply (zenon_L261_); trivial. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H6d ]. % 4.69/4.90 apply (zenon_L265_); trivial. % 4.69/4.90 exact (zenon_H145 zenon_H6d). % 4.69/4.90 (* end of lemma zenon_L272_ *) % 4.69/4.90 assert (zenon_L273_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e3)) = (e1)) -> False). % 4.69/4.90 do 0 intro. intros zenon_H1c7 zenon_H82 zenon_H98 zenon_H25 zenon_Hd0 zenon_H4b zenon_H179 zenon_H16c zenon_H4c zenon_H87. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H42 | zenon_intro zenon_H1c8 ]. % 4.69/4.90 apply (zenon_L31_); trivial. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H1a1 | zenon_intro zenon_H1c9 ]. % 4.69/4.90 apply (zenon_L244_); trivial. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H43 | zenon_intro zenon_H80 ]. % 4.69/4.90 exact (zenon_H179 zenon_H43). % 4.69/4.90 apply (zenon_L268_); trivial. % 4.69/4.90 (* end of lemma zenon_L273_ *) % 4.69/4.90 assert (zenon_L274_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> False). % 4.69/4.90 do 0 intro. intros zenon_H94 zenon_H87 zenon_H16c zenon_H179 zenon_H4b zenon_Hd0 zenon_H25 zenon_H82 zenon_H1c7 zenon_H9d zenon_Hf1 zenon_H4c zenon_H85. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H98 | zenon_intro zenon_H97 ]. % 4.69/4.90 apply (zenon_L273_); trivial. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H9a | zenon_intro zenon_H99 ]. % 4.69/4.90 apply (zenon_L270_); trivial. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H99); [ zenon_intro zenon_H51 | zenon_intro zenon_H81 ]. % 4.69/4.90 exact (zenon_H4c zenon_H51). % 4.69/4.90 exact (zenon_H85 zenon_H81). % 4.69/4.90 (* end of lemma zenon_L274_ *) % 4.69/4.90 assert (zenon_L275_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e2) (e3)) = (e1)) -> False). % 4.69/4.90 do 0 intro. intros zenon_H89 zenon_H87 zenon_Hd5. % 4.69/4.90 cut (((op (e0) (e3)) = (e1)) = ((op (e0) (e3)) = (op (e2) (e3)))). % 4.69/4.90 intro zenon_D_pnotp. % 4.69/4.90 apply zenon_H89. % 4.69/4.90 rewrite <- zenon_D_pnotp. % 4.69/4.90 exact zenon_H87. % 4.69/4.90 cut (((e1) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H13f]. % 4.69/4.90 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 4.69/4.90 congruence. % 4.69/4.90 apply zenon_H6f. apply refl_equal. % 4.69/4.90 apply zenon_H13f. apply sym_equal. exact zenon_Hd5. % 4.69/4.90 (* end of lemma zenon_L275_ *) % 4.69/4.90 assert (zenon_L276_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 4.69/4.90 do 0 intro. intros zenon_H16b zenon_Hb9 zenon_H42 zenon_H85 zenon_H4c zenon_H9d zenon_H1c7 zenon_H82 zenon_H25 zenon_Hd0 zenon_H4b zenon_H179 zenon_H94 zenon_H16c zenon_H89 zenon_H87. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H16d ]. % 4.69/4.90 apply (zenon_L100_); trivial. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H16e ]. % 4.69/4.90 apply (zenon_L274_); trivial. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_H48 | zenon_intro zenon_Hd5 ]. % 4.69/4.90 exact (zenon_H16c zenon_H48). % 4.69/4.90 apply (zenon_L275_); trivial. % 4.69/4.90 (* end of lemma zenon_L276_ *) % 4.69/4.90 assert (zenon_L277_ : (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> False). % 4.69/4.90 do 0 intro. intros zenon_H1e1 zenon_Hb8 zenon_H192. % 4.69/4.90 cut (((op (e0) (e2)) = (e1)) = ((op (e0) (e2)) = (op (e3) (e2)))). % 4.69/4.90 intro zenon_D_pnotp. % 4.69/4.90 apply zenon_H1e1. % 4.69/4.90 rewrite <- zenon_D_pnotp. % 4.69/4.90 exact zenon_Hb8. % 4.69/4.90 cut (((e1) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H193]. % 4.69/4.90 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H134]. % 4.69/4.90 congruence. % 4.69/4.90 apply zenon_H134. apply refl_equal. % 4.69/4.90 apply zenon_H193. apply sym_equal. exact zenon_H192. % 4.69/4.90 (* end of lemma zenon_L277_ *) % 4.69/4.90 assert (zenon_L278_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 4.69/4.90 do 0 intro. intros zenon_H1e2 zenon_Hb9 zenon_H2c zenon_H2b zenon_H13c zenon_Hbd zenon_H54 zenon_H28 zenon_Hb8 zenon_H1e1 zenon_H140. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H123 | zenon_intro zenon_H1e3 ]. % 4.69/4.90 apply (zenon_L86_); trivial. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_Hfa | zenon_intro zenon_H1e4 ]. % 4.69/4.90 apply (zenon_L234_); trivial. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H192 | zenon_intro zenon_H72 ]. % 4.69/4.90 apply (zenon_L277_); trivial. % 4.69/4.90 exact (zenon_H140 zenon_H72). % 4.69/4.90 (* end of lemma zenon_L278_ *) % 4.69/4.90 assert (zenon_L279_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((e1) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> False). % 4.69/4.90 do 0 intro. intros zenon_H118 zenon_H5b zenon_H140 zenon_H1e1 zenon_H1e2 zenon_H101 zenon_Hb9 zenon_H36 zenon_H85 zenon_H4c zenon_H9d zenon_H1c7 zenon_H82 zenon_H25 zenon_Hd0 zenon_H4b zenon_H179 zenon_H16c zenon_H94 zenon_H28 zenon_H54 zenon_Hbd zenon_H13c zenon_H2b zenon_H2c. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H5a | zenon_intro zenon_H119 ]. % 4.69/4.90 exact (zenon_H5b zenon_H5a). % 4.69/4.90 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H9c | zenon_intro zenon_H11c ]. % 4.69/4.90 apply (zenon_L92_); trivial. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H87 ]. % 4.69/4.90 apply (zenon_L278_); trivial. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H9c | zenon_intro zenon_H10a ]. % 4.69/4.90 apply (zenon_L92_); trivial. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H10a); [ zenon_intro zenon_H3e | zenon_intro zenon_H10b ]. % 4.69/4.90 exact (zenon_H36 zenon_H3e). % 4.69/4.90 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hfa ]. % 4.69/4.90 apply (zenon_L274_); trivial. % 4.69/4.90 apply (zenon_L234_); trivial. % 4.69/4.90 (* end of lemma zenon_L279_ *) % 4.69/4.90 assert (zenon_L280_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (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) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> False). % 4.69/4.90 do 0 intro. intros zenon_H1d zenon_H2c zenon_H2b zenon_H13c zenon_H54 zenon_H28 zenon_H94 zenon_H16c zenon_H179 zenon_H4b zenon_Hd0 zenon_H82 zenon_H1c7 zenon_H9d zenon_H4c zenon_H85 zenon_H36 zenon_Hb9 zenon_H101 zenon_H1e2 zenon_H1e1 zenon_H140 zenon_H5b zenon_H118 zenon_H145 zenon_H75 zenon_H198 zenon_H1de zenon_H16b zenon_H89 zenon_Hbe zenon_H1ab zenon_H1e zenon_H114 zenon_H20 zenon_H21. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ]. % 4.69/4.90 exact (zenon_H1e zenon_H23). % 4.69/4.90 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ]. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H114); [ zenon_intro zenon_H23 | zenon_intro zenon_H115 ]. % 4.69/4.90 exact (zenon_H1e zenon_H23). % 4.69/4.90 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H34 | zenon_intro zenon_H116 ]. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H5a | zenon_intro zenon_H119 ]. % 4.69/4.90 exact (zenon_H5b zenon_H5a). % 4.69/4.90 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H9c | zenon_intro zenon_H11c ]. % 4.69/4.90 apply (zenon_L92_); trivial. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H87 ]. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H1de); [ zenon_intro zenon_Hbd | zenon_intro zenon_H1df ]. % 4.69/4.90 apply (zenon_L36_); trivial. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_H10e | zenon_intro zenon_H1e0 ]. % 4.69/4.90 apply (zenon_L261_); trivial. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H6d ]. % 4.69/4.90 apply (zenon_L265_); trivial. % 4.69/4.90 exact (zenon_H145 zenon_H6d). % 4.69/4.90 apply (zenon_L269_); trivial. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H42 | zenon_intro zenon_Hbd ]. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H5a | zenon_intro zenon_H119 ]. % 4.69/4.90 exact (zenon_H5b zenon_H5a). % 4.69/4.90 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H9c | zenon_intro zenon_H11c ]. % 4.69/4.90 apply (zenon_L92_); trivial. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H87 ]. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H9c | zenon_intro zenon_H10a ]. % 4.69/4.90 apply (zenon_L92_); trivial. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H10a); [ zenon_intro zenon_H3e | zenon_intro zenon_H10b ]. % 4.69/4.90 exact (zenon_H36 zenon_H3e). % 4.69/4.90 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hfa ]. % 4.69/4.90 apply (zenon_L271_); trivial. % 4.69/4.90 apply (zenon_L272_); trivial. % 4.69/4.90 apply (zenon_L276_); trivial. % 4.69/4.90 apply (zenon_L279_); trivial. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H24); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 4.69/4.90 exact (zenon_H20 zenon_H27). % 4.69/4.90 exact (zenon_H21 zenon_H26). % 4.69/4.90 (* end of lemma zenon_L280_ *) % 4.69/4.90 assert (zenon_L281_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e1) (e3)) = (e3)) -> False). % 4.69/4.90 do 0 intro. intros zenon_H86 zenon_H8c zenon_Hdb. % 4.69/4.90 cut (((op (e0) (e3)) = (e3)) = ((op (e0) (e3)) = (op (e1) (e3)))). % 4.69/4.90 intro zenon_D_pnotp. % 4.69/4.90 apply zenon_H86. % 4.69/4.90 rewrite <- zenon_D_pnotp. % 4.69/4.90 exact zenon_H8c. % 4.69/4.90 cut (((e3) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1e5]. % 4.69/4.90 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 4.69/4.90 congruence. % 4.69/4.90 apply zenon_H6f. apply refl_equal. % 4.69/4.90 apply zenon_H1e5. apply sym_equal. exact zenon_Hdb. % 4.69/4.90 (* end of lemma zenon_L281_ *) % 4.69/4.90 assert (zenon_L282_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e0)) = (e2)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 4.69/4.90 do 0 intro. intros zenon_H166 zenon_H13c zenon_H7e zenon_H38 zenon_Hb6 zenon_Hb8 zenon_H86 zenon_H8c. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H156 | zenon_intro zenon_H169 ]. % 4.69/4.90 apply (zenon_L119_); trivial. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H3f | zenon_intro zenon_H16a ]. % 4.69/4.90 exact (zenon_H38 zenon_H3f). % 4.69/4.90 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H162 | zenon_intro zenon_Hdb ]. % 4.69/4.90 apply (zenon_L146_); trivial. % 4.69/4.90 apply (zenon_L281_); trivial. % 4.69/4.90 (* end of lemma zenon_L282_ *) % 4.69/4.90 assert (zenon_L283_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (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))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 4.69/4.90 do 0 intro. intros zenon_H100 zenon_H86 zenon_H38 zenon_H7e zenon_H13c zenon_H166 zenon_H54 zenon_H104 zenon_H103 zenon_H82 zenon_H25 zenon_H9d zenon_Hb8 zenon_H75 zenon_H145 zenon_H140 zenon_H6c zenon_H2c. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hb6 | zenon_intro zenon_H105 ]. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_H108 | zenon_intro zenon_H107 ]. % 4.69/4.90 exact (zenon_H104 zenon_H108). % 4.69/4.90 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H109 ]. % 4.69/4.90 apply (zenon_L94_); trivial. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Hed | zenon_intro zenon_H8c ]. % 4.69/4.90 apply (zenon_L144_); trivial. % 4.69/4.90 apply (zenon_L282_); trivial. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H5e | zenon_intro zenon_H106 ]. % 4.69/4.90 apply (zenon_L148_); trivial. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_H92 | zenon_intro zenon_H8a ]. % 4.69/4.90 apply (zenon_L149_); trivial. % 4.69/4.90 apply (zenon_L252_); trivial. % 4.69/4.90 (* end of lemma zenon_L283_ *) % 4.69/4.90 assert (zenon_L284_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (e0)) = (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) (e1)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> False). % 4.69/4.90 do 0 intro. intros zenon_H7b zenon_H8c zenon_H86 zenon_Hb8 zenon_Hb6 zenon_H38 zenon_H13c zenon_H166 zenon_H36 zenon_H195 zenon_H135. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H7b); [ zenon_intro zenon_H7e | zenon_intro zenon_H7d ]. % 4.69/4.90 apply (zenon_L282_); trivial. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H7d); [ zenon_intro zenon_H3e | zenon_intro zenon_H7f ]. % 4.69/4.90 exact (zenon_H36 zenon_H3e). % 4.69/4.90 apply (zenon_or_s _ _ zenon_H7f); [ zenon_intro zenon_H47 | zenon_intro zenon_H71 ]. % 4.69/4.90 exact (zenon_H195 zenon_H47). % 4.69/4.90 exact (zenon_H135 zenon_H71). % 4.69/4.90 (* end of lemma zenon_L284_ *) % 4.69/4.90 assert (zenon_L285_ : (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> ((op (e3) (e1)) = (e1)) -> False). % 4.69/4.90 do 0 intro. intros zenon_Haf zenon_H123 zenon_Hfa. % 4.69/4.90 cut (((op (e3) (e0)) = (e1)) = ((op (e3) (e0)) = (op (e3) (e1)))). % 4.69/4.90 intro zenon_D_pnotp. % 4.69/4.90 apply zenon_Haf. % 4.69/4.90 rewrite <- zenon_D_pnotp. % 4.69/4.90 exact zenon_H123. % 4.69/4.90 cut (((e1) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1e6]. % 4.69/4.90 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 4.69/4.90 congruence. % 4.69/4.90 apply zenon_Hb2. apply refl_equal. % 4.69/4.90 apply zenon_H1e6. apply sym_equal. exact zenon_Hfa. % 4.69/4.90 (* end of lemma zenon_L285_ *) % 4.69/4.90 assert (zenon_L286_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> False). % 4.69/4.90 do 0 intro. intros zenon_H101 zenon_Hb9 zenon_H25 zenon_H36 zenon_H85 zenon_H4c zenon_H9d zenon_H42 zenon_H82 zenon_H94 zenon_Haf zenon_H123. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H9c | zenon_intro zenon_H10a ]. % 4.69/4.90 apply (zenon_L92_); trivial. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H10a); [ zenon_intro zenon_H3e | zenon_intro zenon_H10b ]. % 4.69/4.90 exact (zenon_H36 zenon_H3e). % 4.69/4.90 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hfa ]. % 4.69/4.90 apply (zenon_L271_); trivial. % 4.69/4.90 apply (zenon_L285_); trivial. % 4.69/4.90 (* end of lemma zenon_L286_ *) % 4.69/4.90 assert (zenon_L287_ : ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (((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 (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (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 (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> False). % 4.69/4.90 do 0 intro. intros zenon_H153 zenon_H11f zenon_H1e zenon_H114 zenon_H101 zenon_H28 zenon_Hef zenon_H195 zenon_H5b zenon_Hb9 zenon_H7b zenon_H135 zenon_H132 zenon_H36 zenon_H7c zenon_H137 zenon_Hb4 zenon_H82 zenon_Hb3 zenon_H12e zenon_H113 zenon_H9d zenon_H54 zenon_Hfd zenon_H13c zenon_H103 zenon_H95 zenon_Hdf zenon_H140 zenon_H13e zenon_H100 zenon_H118 zenon_H20 zenon_H21 zenon_H1d zenon_H171 zenon_H165 zenon_H173 zenon_H6c zenon_H152 zenon_H117 zenon_H142 zenon_H70 zenon_H75 zenon_Hd0 zenon_H94 zenon_H1ca zenon_Hd7 zenon_H1c7 zenon_H170 zenon_H1ab zenon_He9 zenon_H172 zenon_H1cb zenon_H1cc zenon_H11e. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H85 | zenon_intro zenon_H104 ]. % 4.69/4.90 apply (zenon_L259_); trivial. % 4.69/4.90 apply (zenon_L73_); trivial. % 4.69/4.90 (* end of lemma zenon_L287_ *) % 4.69/4.90 assert (zenon_L288_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 4.69/4.90 do 0 intro. intros zenon_H100 zenon_H13c zenon_Hfd zenon_H25 zenon_H54 zenon_H12e zenon_H85 zenon_H113 zenon_H103 zenon_H1c7 zenon_H82 zenon_Hd0 zenon_H4b zenon_H179 zenon_H16c zenon_H4c zenon_H7b zenon_H36 zenon_H195 zenon_H135 zenon_Hb4 zenon_Hb3 zenon_H87 zenon_H9d. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hb6 | zenon_intro zenon_H105 ]. % 4.69/4.90 exact (zenon_Hb4 zenon_Hb6). % 4.69/4.90 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H5e | zenon_intro zenon_H106 ]. % 4.69/4.90 apply (zenon_L148_); trivial. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_H92 | zenon_intro zenon_H8a ]. % 4.69/4.90 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hb5 ]. % 4.69/4.90 exact (zenon_Hb4 zenon_Hb6). % 4.69/4.90 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hb7 ]. % 4.69/4.90 apply (zenon_L232_); trivial. % 4.69/4.90 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H98 | zenon_intro zenon_Hb0 ]. % 4.69/4.90 apply (zenon_L273_); trivial. % 4.69/4.90 apply (zenon_L231_); trivial. % 4.69/4.90 apply (zenon_L79_); trivial. % 4.69/4.90 (* end of lemma zenon_L288_ *) % 4.69/4.90 assert (zenon_L289_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> False). % 4.69/4.90 do 0 intro. intros zenon_H1d zenon_H1e zenon_H9d zenon_Hb3 zenon_Hb4 zenon_H135 zenon_H195 zenon_H36 zenon_H7b zenon_H4c zenon_H16c zenon_H179 zenon_H4b zenon_Hd0 zenon_H82 zenon_H1c7 zenon_H103 zenon_H113 zenon_H85 zenon_H12e zenon_H54 zenon_Hfd zenon_H13c zenon_H100 zenon_H7c zenon_H132 zenon_Hb9 zenon_H5b zenon_H118 zenon_H20 zenon_H21. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ]. % 4.69/4.90 exact (zenon_H1e zenon_H23). % 4.69/4.90 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ]. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H5a | zenon_intro zenon_H119 ]. % 4.69/4.90 exact (zenon_H5b zenon_H5a). % 4.69/4.90 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H9c | zenon_intro zenon_H11c ]. % 4.69/4.90 apply (zenon_L92_); trivial. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H87 ]. % 4.69/4.90 apply (zenon_L88_); trivial. % 4.69/4.90 apply (zenon_L288_); trivial. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H24); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 4.69/4.90 exact (zenon_H20 zenon_H27). % 4.69/4.90 exact (zenon_H21 zenon_H26). % 4.69/4.90 (* end of lemma zenon_L289_ *) % 4.69/4.90 assert (zenon_L290_ : ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (e1))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((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)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> False). % 4.69/4.90 do 0 intro. intros zenon_H1bd zenon_H165 zenon_H1d zenon_H21 zenon_H20 zenon_H5b zenon_Hb9 zenon_H7b zenon_H135 zenon_H132 zenon_H36 zenon_H7c zenon_H100 zenon_H195 zenon_H9d zenon_H1c7 zenon_H16c zenon_H4b zenon_H179 zenon_Hd0 zenon_H103 zenon_H13c zenon_Hfd zenon_H54 zenon_H113 zenon_H12e zenon_Hb3 zenon_H82 zenon_Hb4 zenon_H118 zenon_H1e zenon_H11f zenon_H152. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H1bd); [ zenon_intro zenon_H4c | zenon_intro zenon_H37 ]. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H85 | zenon_intro zenon_H104 ]. % 4.69/4.90 apply (zenon_L289_); trivial. % 4.69/4.90 apply (zenon_L73_); trivial. % 4.69/4.90 apply (zenon_L240_); trivial. % 4.69/4.90 (* end of lemma zenon_L290_ *) % 4.69/4.90 assert (zenon_L291_ : ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (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 (e1) (e1)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((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))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> False). % 4.69/4.90 do 0 intro. intros zenon_H1e7 zenon_H4b zenon_H16c zenon_H1bd zenon_H11e zenon_H1cc zenon_H1cb zenon_H172 zenon_He9 zenon_H1ab zenon_H170 zenon_H1c7 zenon_Hd7 zenon_H1ca zenon_H94 zenon_Hd0 zenon_H75 zenon_H70 zenon_H142 zenon_H117 zenon_H152 zenon_H6c zenon_H173 zenon_H165 zenon_H171 zenon_H1d zenon_H21 zenon_H20 zenon_H118 zenon_H100 zenon_H13e zenon_H140 zenon_Hdf zenon_H103 zenon_H13c zenon_Hfd zenon_H54 zenon_H9d zenon_H113 zenon_H12e zenon_Hb3 zenon_H82 zenon_Hb4 zenon_H137 zenon_H7c zenon_H36 zenon_H132 zenon_H7b zenon_Hb9 zenon_H5b zenon_Hef zenon_H28 zenon_H101 zenon_H114 zenon_H1e zenon_H11f zenon_H153. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H1e7); [ zenon_intro zenon_H195 | zenon_intro zenon_H37 ]. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H135 | zenon_intro zenon_H104 ]. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H95 | zenon_intro zenon_H179 ]. % 4.69/4.90 apply (zenon_L287_); trivial. % 4.69/4.90 apply (zenon_L290_); trivial. % 4.69/4.90 apply (zenon_L73_); trivial. % 4.69/4.90 apply (zenon_L258_); trivial. % 4.69/4.90 (* end of lemma zenon_L291_ *) % 4.69/4.90 assert (zenon_L292_ : ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (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 (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((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)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> False). % 4.69/4.90 do 0 intro. intros zenon_H1e7 zenon_H173 zenon_H6c zenon_H137 zenon_Hdf zenon_H140 zenon_H13e zenon_H117 zenon_H142 zenon_H70 zenon_H75 zenon_H114 zenon_H94 zenon_H153 zenon_H1ca zenon_Hd7 zenon_H170 zenon_H1ab zenon_He9 zenon_H172 zenon_H1cb zenon_H1cc zenon_H1bd zenon_H165 zenon_H1d zenon_H21 zenon_H20 zenon_H5b zenon_Hb9 zenon_H7b zenon_H132 zenon_H36 zenon_H7c zenon_H100 zenon_H9d zenon_H1c7 zenon_H16c zenon_H4b zenon_H179 zenon_Hd0 zenon_H103 zenon_H13c zenon_Hfd zenon_H54 zenon_H113 zenon_H12e zenon_Hb3 zenon_H82 zenon_Hb4 zenon_H118 zenon_H1e zenon_H11f zenon_H152 zenon_H171. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H1e7); [ zenon_intro zenon_H195 | zenon_intro zenon_H37 ]. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H135 | zenon_intro zenon_H104 ]. % 4.69/4.90 apply (zenon_L290_); trivial. % 4.69/4.90 apply (zenon_L73_); trivial. % 4.69/4.90 apply (zenon_L257_); trivial. % 4.69/4.90 (* end of lemma zenon_L292_ *) % 4.69/4.90 assert (zenon_L293_ : ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 4.69/4.90 do 0 intro. intros zenon_H153 zenon_H11f zenon_H1e zenon_H118 zenon_Hb3 zenon_H12e zenon_H113 zenon_H85 zenon_H54 zenon_Hfd zenon_H13c zenon_H103 zenon_Hd0 zenon_H179 zenon_H4b zenon_H4c zenon_H16c zenon_H1c7 zenon_H36 zenon_H195 zenon_H135 zenon_H7b zenon_Hb4 zenon_H82 zenon_H9d zenon_H75 zenon_H6c zenon_H140 zenon_H145 zenon_H100 zenon_Hb9 zenon_H5b zenon_H20 zenon_H21 zenon_H1d. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H2c | zenon_intro zenon_H104 ]. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ]. % 4.69/4.90 exact (zenon_H1e zenon_H23). % 4.69/4.90 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ]. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H5a | zenon_intro zenon_H119 ]. % 4.69/4.90 exact (zenon_H5b zenon_H5a). % 4.69/4.90 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H9c | zenon_intro zenon_H11c ]. % 4.69/4.90 apply (zenon_L92_); trivial. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H87 ]. % 4.69/4.90 apply (zenon_L253_); trivial. % 4.69/4.90 apply (zenon_L288_); trivial. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H24); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 4.69/4.90 exact (zenon_H20 zenon_H27). % 4.69/4.90 exact (zenon_H21 zenon_H26). % 4.69/4.90 apply (zenon_L73_); trivial. % 4.69/4.90 (* end of lemma zenon_L293_ *) % 4.69/4.90 assert (zenon_L294_ : ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> False). % 4.69/4.90 do 0 intro. intros zenon_H1bd zenon_H132 zenon_H165 zenon_H153 zenon_H11f zenon_H1e zenon_H118 zenon_Hb3 zenon_H12e zenon_H113 zenon_H54 zenon_Hfd zenon_H13c zenon_H103 zenon_Hd0 zenon_H179 zenon_H4b zenon_H16c zenon_H1c7 zenon_H36 zenon_H195 zenon_H135 zenon_H7b zenon_Hb4 zenon_H82 zenon_H9d zenon_H75 zenon_H6c zenon_H140 zenon_H145 zenon_H100 zenon_Hb9 zenon_H5b zenon_H20 zenon_H21 zenon_H1d zenon_H152. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H1bd); [ zenon_intro zenon_H4c | zenon_intro zenon_H37 ]. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H85 | zenon_intro zenon_H104 ]. % 4.69/4.90 apply (zenon_L293_); trivial. % 4.69/4.90 apply (zenon_L73_); trivial. % 4.69/4.90 apply (zenon_L254_); trivial. % 4.69/4.90 (* end of lemma zenon_L294_ *) % 4.69/4.90 assert (zenon_L295_ : ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> False). % 4.69/4.90 do 0 intro. intros zenon_H1e7 zenon_H1cb zenon_H1bd zenon_H132 zenon_H165 zenon_H153 zenon_H11f zenon_H1e zenon_H118 zenon_Hb3 zenon_H12e zenon_H113 zenon_H54 zenon_Hfd zenon_H13c zenon_H103 zenon_Hd0 zenon_H179 zenon_H4b zenon_H16c zenon_H1c7 zenon_H36 zenon_H7b zenon_Hb4 zenon_H82 zenon_H9d zenon_H75 zenon_H6c zenon_H140 zenon_H145 zenon_H100 zenon_Hb9 zenon_H5b zenon_H20 zenon_H21 zenon_H1d zenon_H152 zenon_H171. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H1e7); [ zenon_intro zenon_H195 | zenon_intro zenon_H37 ]. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H135 | zenon_intro zenon_H104 ]. % 4.69/4.90 apply (zenon_L294_); trivial. % 4.69/4.90 apply (zenon_L73_); trivial. % 4.69/4.90 apply (zenon_L255_); trivial. % 4.69/4.90 (* end of lemma zenon_L295_ *) % 4.69/4.90 assert (zenon_L296_ : ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (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 (e1) (e1)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((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))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> False). % 4.69/4.90 do 0 intro. intros zenon_H122 zenon_H1e7 zenon_H4b zenon_H16c zenon_H1bd zenon_H11e zenon_H1cc zenon_H1cb zenon_H172 zenon_He9 zenon_H1ab zenon_H170 zenon_H1c7 zenon_Hd7 zenon_H1ca zenon_H94 zenon_Hd0 zenon_H75 zenon_H70 zenon_H142 zenon_H117 zenon_H152 zenon_H6c zenon_H173 zenon_H165 zenon_H171 zenon_H1d zenon_H20 zenon_H118 zenon_H100 zenon_H13e zenon_H140 zenon_Hdf zenon_H103 zenon_H13c zenon_Hfd zenon_H54 zenon_H9d zenon_H113 zenon_H12e zenon_Hb3 zenon_H82 zenon_Hb4 zenon_H137 zenon_H36 zenon_H132 zenon_H7b zenon_Hb9 zenon_H5b zenon_Hef zenon_H28 zenon_H101 zenon_H114 zenon_H1e zenon_H11f zenon_H153 zenon_H1c0. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_H21 | zenon_intro zenon_H104 ]. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H1c0); [ zenon_intro zenon_H7c | zenon_intro zenon_H179 ]. % 4.69/4.90 apply (zenon_L291_); trivial. % 4.69/4.90 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H7c | zenon_intro zenon_H145 ]. % 4.69/4.90 apply (zenon_L292_); trivial. % 4.69/4.90 apply (zenon_L295_); trivial. % 4.69/4.90 apply (zenon_L73_); trivial. % 4.69/4.90 (* end of lemma zenon_L296_ *) % 4.69/4.90 assert (zenon_L297_ : ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (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 (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((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)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> False). % 4.69/4.91 do 0 intro. intros zenon_H122 zenon_H171 zenon_H152 zenon_H1d zenon_H137 zenon_Hb3 zenon_H82 zenon_Hdf zenon_H140 zenon_H13e zenon_H117 zenon_H142 zenon_H70 zenon_H75 zenon_H113 zenon_H114 zenon_H5b zenon_Hb9 zenon_H7b zenon_H132 zenon_H36 zenon_H100 zenon_H12e zenon_H76 zenon_H9d zenon_H54 zenon_Hfd zenon_H13c zenon_H103 zenon_Hd0 zenon_H4c zenon_H94 zenon_Hb4 zenon_H118 zenon_H1e zenon_H11f zenon_H153 zenon_H1ca zenon_Hd7 zenon_H1c7 zenon_H170 zenon_H1ab zenon_He9 zenon_H172 zenon_H1c0 zenon_H173 zenon_H174. % 4.69/4.91 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_H21 | zenon_intro zenon_H104 ]. % 4.69/4.91 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H7c | zenon_intro zenon_Hc3 ]. % 4.69/4.91 apply (zenon_L250_); trivial. % 4.69/4.91 apply (zenon_or_s _ _ zenon_H1c0); [ zenon_intro zenon_H7c | zenon_intro zenon_H179 ]. % 4.69/4.91 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H135 | zenon_intro zenon_H104 ]. % 4.69/4.91 apply (zenon_L249_); trivial. % 4.69/4.91 apply (zenon_L73_); trivial. % 4.69/4.91 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H7c | zenon_intro zenon_H145 ]. % 4.69/4.91 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H135 | zenon_intro zenon_H104 ]. % 4.69/4.91 apply (zenon_L248_); trivial. % 4.69/4.91 apply (zenon_L73_); trivial. % 4.69/4.91 apply (zenon_L130_); trivial. % 4.69/4.91 apply (zenon_L73_); trivial. % 4.69/4.91 (* end of lemma zenon_L297_ *) % 4.69/4.91 assert (zenon_L298_ : ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (((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 (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (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))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (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 (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> False). % 4.69/4.91 do 0 intro. intros zenon_H175 zenon_H176 zenon_H174 zenon_H177 zenon_H1c0 zenon_H153 zenon_H11f zenon_H1e zenon_H114 zenon_H101 zenon_H28 zenon_Hef zenon_H5b zenon_Hb9 zenon_H7b zenon_H132 zenon_H36 zenon_H137 zenon_Hb4 zenon_H82 zenon_Hb3 zenon_H12e zenon_H113 zenon_H9d zenon_H54 zenon_Hfd zenon_H13c zenon_H103 zenon_Hdf zenon_H140 zenon_H13e zenon_H100 zenon_H118 zenon_H1d zenon_H171 zenon_H165 zenon_H173 zenon_H6c zenon_H152 zenon_H117 zenon_H142 zenon_H70 zenon_H75 zenon_Hd0 zenon_H94 zenon_H1ca zenon_Hd7 zenon_H1c7 zenon_H170 zenon_H1ab zenon_He9 zenon_H172 zenon_H1cb zenon_H1cc zenon_H11e zenon_H1bd zenon_H16c zenon_H4b zenon_H1e7 zenon_H122. % 4.69/4.91 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H20 | zenon_intro zenon_H37 ]. % 4.69/4.91 apply (zenon_L296_); trivial. % 4.69/4.91 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_H20 | zenon_intro zenon_H4c ]. % 4.69/4.91 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_H21 | zenon_intro zenon_H104 ]. % 4.69/4.91 apply (zenon_L258_); trivial. % 4.69/4.91 apply (zenon_L73_); trivial. % 4.69/4.91 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H20 | zenon_intro zenon_H76 ]. % 4.69/4.91 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_H21 | zenon_intro zenon_H104 ]. % 4.69/4.91 apply (zenon_L256_); trivial. % 4.69/4.91 apply (zenon_L73_); trivial. % 4.69/4.91 apply (zenon_L297_); trivial. % 4.69/4.91 (* end of lemma zenon_L298_ *) % 4.69/4.91 assert (zenon_L299_ : ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((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))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((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) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> False). % 4.69/4.91 do 0 intro. intros zenon_H1b6 zenon_H122 zenon_H1e7 zenon_H1bd zenon_H11e zenon_H1cc zenon_H1cb zenon_H172 zenon_He9 zenon_H1ab zenon_H170 zenon_H1c7 zenon_Hd7 zenon_H1ca zenon_H94 zenon_Hd0 zenon_H75 zenon_H70 zenon_H142 zenon_H117 zenon_H152 zenon_H6c zenon_H173 zenon_H165 zenon_H171 zenon_H1d zenon_H118 zenon_H100 zenon_H13e zenon_H140 zenon_Hdf zenon_H103 zenon_H13c zenon_Hfd zenon_H54 zenon_H9d zenon_H113 zenon_H12e zenon_Hb3 zenon_H82 zenon_H137 zenon_H36 zenon_H132 zenon_H7b zenon_Hb9 zenon_H5b zenon_Hef zenon_H28 zenon_H101 zenon_H114 zenon_H1e zenon_H11f zenon_H153 zenon_H1c0 zenon_H177 zenon_H174 zenon_H176 zenon_H175 zenon_H179 zenon_H16c zenon_H4d zenon_H4b. % 4.69/4.91 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H4c | zenon_intro zenon_Hb4 ]. % 4.69/4.91 apply (zenon_L193_); trivial. % 4.69/4.91 apply (zenon_L298_); trivial. % 4.69/4.91 (* end of lemma zenon_L299_ *) % 4.69/4.91 assert (zenon_L300_ : ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (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 (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (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 (e1) (e1)) = (e0))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 4.69/4.91 do 0 intro. intros zenon_H1c5 zenon_H175 zenon_H176 zenon_H174 zenon_H177 zenon_H1c0 zenon_H153 zenon_H11f zenon_Hef zenon_H132 zenon_Hb3 zenon_H12e zenon_H113 zenon_H171 zenon_H165 zenon_H173 zenon_H152 zenon_H117 zenon_H142 zenon_H70 zenon_H1ca zenon_Hd7 zenon_H170 zenon_He9 zenon_H172 zenon_H1cb zenon_H1cc zenon_H11e zenon_H1bd zenon_H1e7 zenon_H122 zenon_H1b6 zenon_H1e zenon_H114 zenon_H1e2 zenon_H1e1 zenon_H2b zenon_H28 zenon_H94 zenon_H85 zenon_Haf zenon_H101 zenon_H16b zenon_H89 zenon_H5b zenon_Hb9 zenon_H137 zenon_H16c zenon_Hf6 zenon_H194 zenon_H33 zenon_H19d zenon_Hc3 zenon_Hfd zenon_H36 zenon_H195 zenon_H135 zenon_H7b zenon_Hdf zenon_H13e zenon_H103 zenon_H38 zenon_H86 zenon_H166 zenon_H13c zenon_H54 zenon_H104 zenon_H82 zenon_H9d zenon_H75 zenon_H6c zenon_H140 zenon_H145 zenon_H100 zenon_H1c7 zenon_H4c zenon_H4b zenon_H179 zenon_Hd0 zenon_H1ab zenon_H118 zenon_H20 zenon_H21 zenon_H1d. % 4.69/4.91 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H2c | zenon_intro zenon_H4d ]. % 4.69/4.91 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ]. % 4.69/4.91 exact (zenon_H1e zenon_H23). % 4.69/4.91 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ]. % 4.69/4.91 apply (zenon_or_s _ _ zenon_H114); [ zenon_intro zenon_H23 | zenon_intro zenon_H115 ]. % 4.69/4.91 exact (zenon_H1e zenon_H23). % 4.69/4.91 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H34 | zenon_intro zenon_H116 ]. % 4.69/4.91 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H5a | zenon_intro zenon_H119 ]. % 4.69/4.91 exact (zenon_H5b zenon_H5a). % 4.69/4.91 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H9c | zenon_intro zenon_H11c ]. % 4.69/4.91 apply (zenon_L92_); trivial. % 4.69/4.91 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H87 ]. % 4.69/4.91 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_H5a | zenon_intro zenon_H138 ]. % 4.69/4.91 exact (zenon_H5b zenon_H5a). % 4.69/4.91 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_H7e | zenon_intro zenon_H139 ]. % 4.69/4.91 apply (zenon_L283_); trivial. % 4.69/4.91 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H123 ]. % 4.69/4.91 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hb6 | zenon_intro zenon_H105 ]. % 4.69/4.91 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_H108 | zenon_intro zenon_H107 ]. % 4.69/4.91 exact (zenon_H104 zenon_H108). % 4.69/4.91 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H109 ]. % 4.69/4.91 apply (zenon_L94_); trivial. % 4.69/4.91 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Hed | zenon_intro zenon_H8c ]. % 4.69/4.91 apply (zenon_L144_); trivial. % 4.69/4.91 apply (zenon_L284_); trivial. % 4.69/4.91 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H5e | zenon_intro zenon_H106 ]. % 4.69/4.91 apply (zenon_L148_); trivial. % 4.69/4.91 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_H92 | zenon_intro zenon_H8a ]. % 4.69/4.91 apply (zenon_L149_); trivial. % 4.69/4.91 apply (zenon_L98_); trivial. % 4.69/4.91 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hb6 | zenon_intro zenon_H105 ]. % 4.69/4.91 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_H108 | zenon_intro zenon_H107 ]. % 4.69/4.91 exact (zenon_H104 zenon_H108). % 4.69/4.91 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H109 ]. % 4.69/4.91 apply (zenon_L94_); trivial. % 4.69/4.91 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Hed | zenon_intro zenon_H8c ]. % 4.69/4.91 apply (zenon_L151_); trivial. % 4.69/4.91 apply (zenon_L284_); trivial. % 4.69/4.91 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H5e | zenon_intro zenon_H106 ]. % 4.69/4.91 apply (zenon_L164_); trivial. % 4.69/4.91 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_H92 | zenon_intro zenon_H8a ]. % 4.69/4.91 apply (zenon_L149_); trivial. % 4.69/4.91 apply (zenon_L152_); trivial. % 4.69/4.91 apply (zenon_L269_); trivial. % 4.69/4.91 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H42 | zenon_intro zenon_Hbd ]. % 4.69/4.91 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H5a | zenon_intro zenon_H119 ]. % 4.69/4.91 exact (zenon_H5b zenon_H5a). % 4.69/4.91 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H9c | zenon_intro zenon_H11c ]. % 4.69/4.91 apply (zenon_L92_); trivial. % 4.69/4.91 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H87 ]. % 4.69/4.91 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_H5a | zenon_intro zenon_H138 ]. % 4.69/4.91 exact (zenon_H5b zenon_H5a). % 4.69/4.91 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_H7e | zenon_intro zenon_H139 ]. % 4.69/4.91 apply (zenon_L283_); trivial. % 4.69/4.91 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H123 ]. % 4.69/4.91 apply (zenon_L100_); trivial. % 4.69/4.91 apply (zenon_L286_); trivial. % 4.69/4.91 apply (zenon_L276_); trivial. % 4.69/4.91 apply (zenon_L279_); trivial. % 4.69/4.91 apply (zenon_or_s _ _ zenon_H24); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 4.69/4.91 exact (zenon_H20 zenon_H27). % 4.69/4.91 exact (zenon_H21 zenon_H26). % 4.69/4.91 apply (zenon_L299_); trivial. % 4.69/4.91 (* end of lemma zenon_L300_ *) % 4.69/4.91 assert (zenon_L301_ : ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (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))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 4.69/4.91 do 0 intro. intros zenon_H1e8 zenon_H100 zenon_H6c zenon_H104 zenon_H166 zenon_H86 zenon_H103 zenon_H13e zenon_Hdf zenon_H7b zenon_H135 zenon_H195 zenon_Hfd zenon_Hc3 zenon_H19d zenon_H33 zenon_H194 zenon_Hf6 zenon_H137 zenon_Haf zenon_H1b6 zenon_H122 zenon_H1e7 zenon_H1bd zenon_H11e zenon_H1cc zenon_H1cb zenon_H172 zenon_He9 zenon_H170 zenon_Hd7 zenon_H1ca zenon_H70 zenon_H142 zenon_H117 zenon_H152 zenon_H173 zenon_H165 zenon_H171 zenon_H113 zenon_H12e zenon_Hb3 zenon_H132 zenon_Hef zenon_H11f zenon_H153 zenon_H1c0 zenon_H177 zenon_H174 zenon_H176 zenon_H175 zenon_H1c5 zenon_H1e zenon_H114 zenon_H1e2 zenon_H1e1 zenon_H101 zenon_H28 zenon_H2b zenon_H13c zenon_H54 zenon_H82 zenon_H9d zenon_H85 zenon_H94 zenon_H36 zenon_H16b zenon_H89 zenon_H5b zenon_Hb9 zenon_H1de zenon_H145 zenon_H140 zenon_H75 zenon_H198 zenon_Hbe zenon_H1c7 zenon_H16c zenon_H4c zenon_H4b zenon_H179 zenon_Hd0 zenon_H1ab zenon_H118 zenon_H20 zenon_H21 zenon_H1d. % 4.69/4.91 apply (zenon_or_s _ _ zenon_H1e8); [ zenon_intro zenon_H2c | zenon_intro zenon_H38 ]. % 4.69/4.91 apply (zenon_L280_); trivial. % 4.69/4.91 apply (zenon_L300_); trivial. % 4.69/4.91 (* end of lemma zenon_L301_ *) % 4.69/4.91 assert (zenon_L302_ : ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (e2))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((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 (e2) (e2)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (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 (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (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 (e1) (e1)) = (e0))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((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))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> False). % 4.69/4.91 do 0 intro. intros zenon_H19a zenon_H1d zenon_H21 zenon_H20 zenon_H118 zenon_H1ab zenon_Hd0 zenon_H179 zenon_H4b zenon_H4c zenon_H16c zenon_H1c7 zenon_Hbe zenon_H198 zenon_H75 zenon_H140 zenon_H145 zenon_H1de zenon_Hb9 zenon_H5b zenon_H89 zenon_H16b zenon_H36 zenon_H94 zenon_H85 zenon_H9d zenon_H82 zenon_H54 zenon_H13c zenon_H28 zenon_H101 zenon_H1e1 zenon_H1e2 zenon_H114 zenon_H1e zenon_H1c5 zenon_H175 zenon_H176 zenon_H174 zenon_H177 zenon_H1c0 zenon_H153 zenon_H11f zenon_Hef zenon_H132 zenon_Hb3 zenon_H12e zenon_H113 zenon_H171 zenon_H165 zenon_H173 zenon_H152 zenon_H117 zenon_H142 zenon_H70 zenon_H1ca zenon_Hd7 zenon_H170 zenon_He9 zenon_H172 zenon_H1cb zenon_H1cc zenon_H11e zenon_H1bd zenon_H1e7 zenon_H122 zenon_H1b6 zenon_Haf zenon_H137 zenon_Hf6 zenon_H194 zenon_H33 zenon_H19d zenon_Hc3 zenon_Hfd zenon_H195 zenon_H135 zenon_H7b zenon_Hdf zenon_H13e zenon_H103 zenon_H86 zenon_H166 zenon_H104 zenon_H6c zenon_H100 zenon_H1e8. % 4.69/4.91 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H2b | zenon_intro zenon_Hb4 ]. % 4.69/4.91 apply (zenon_L301_); trivial. % 4.69/4.91 apply (zenon_L293_); trivial. % 4.69/4.91 (* end of lemma zenon_L302_ *) % 4.69/4.91 assert (zenon_L303_ : ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> (((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)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((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 (e2) (e2)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((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 (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> False). % 4.69/4.91 do 0 intro. intros zenon_H1b9 zenon_H1e8 zenon_H166 zenon_H86 zenon_Hc3 zenon_H19d zenon_H33 zenon_Haf zenon_H1b6 zenon_H122 zenon_H1e7 zenon_H1bd zenon_H1c0 zenon_H177 zenon_H174 zenon_H176 zenon_H175 zenon_H1e2 zenon_H1e1 zenon_H16b zenon_H89 zenon_H1de zenon_Hbe zenon_H179 zenon_H1c5 zenon_H18f zenon_H82 zenon_H9d zenon_Hfd zenon_H54 zenon_H100 zenon_H4b zenon_H4c zenon_H186 zenon_H1c4 zenon_H1e zenon_H118 zenon_H101 zenon_H13c zenon_H28 zenon_Hef zenon_H103 zenon_H195 zenon_H16c zenon_Hf6 zenon_H194 zenon_H198 zenon_H104 zenon_H137 zenon_H7c zenon_H36 zenon_H132 zenon_H135 zenon_H7b zenon_Hb9 zenon_H5b zenon_H20 zenon_H21 zenon_H1d zenon_H11e zenon_H1cc zenon_H1cb zenon_H172 zenon_He9 zenon_H1ab zenon_H170 zenon_H1c7 zenon_Hd7 zenon_H1ca zenon_H94 zenon_Hd0 zenon_H75 zenon_H70 zenon_H142 zenon_H117 zenon_H152 zenon_H6c zenon_H173 zenon_H165 zenon_H171 zenon_H13e zenon_H140 zenon_Hdf zenon_H95 zenon_H85 zenon_H113 zenon_H12e zenon_Hb3 zenon_H114 zenon_H11f zenon_H153 zenon_H19a. % 4.69/4.91 apply (zenon_or_s _ _ zenon_H1b9); [ zenon_intro zenon_H29 | zenon_intro zenon_H145 ]. % 4.69/4.91 apply (zenon_L260_); trivial. % 4.69/4.91 apply (zenon_L302_); trivial. % 4.69/4.91 (* end of lemma zenon_L303_ *) % 4.69/4.91 assert (zenon_L304_ : ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> (~((op (e3) (e0)) = (op (e3) (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)) = (e0))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((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 (e2) (e2)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((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 (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> False). % 4.69/4.91 do 0 intro. intros zenon_H1ba zenon_Hbe zenon_H1de zenon_H89 zenon_H16b zenon_H1e1 zenon_H1e2 zenon_H175 zenon_H176 zenon_H174 zenon_H177 zenon_H1c0 zenon_H1bd zenon_H1e7 zenon_H122 zenon_H1b6 zenon_Haf zenon_H33 zenon_H19d zenon_Hc3 zenon_H86 zenon_H166 zenon_H1e8 zenon_H1b9 zenon_H1c5 zenon_H18f zenon_H82 zenon_H9d zenon_Hfd zenon_H54 zenon_H100 zenon_H4b zenon_H4c zenon_H186 zenon_H1c4 zenon_H1e zenon_H118 zenon_H101 zenon_H13c zenon_H28 zenon_Hef zenon_H103 zenon_H195 zenon_H16c zenon_Hf6 zenon_H194 zenon_H198 zenon_H104 zenon_H137 zenon_H7c zenon_H36 zenon_H132 zenon_H135 zenon_H7b zenon_Hb9 zenon_H5b zenon_H20 zenon_H21 zenon_H1d zenon_H11e zenon_H1cc zenon_H1cb zenon_H172 zenon_He9 zenon_H1ab zenon_H170 zenon_H1c7 zenon_Hd7 zenon_H1ca zenon_H94 zenon_Hd0 zenon_H75 zenon_H70 zenon_H142 zenon_H117 zenon_H152 zenon_H6c zenon_H173 zenon_H165 zenon_H171 zenon_H13e zenon_H140 zenon_Hdf zenon_H95 zenon_H85 zenon_H113 zenon_H12e zenon_Hb3 zenon_H114 zenon_H11f zenon_H153 zenon_H19a. % 4.69/4.91 apply (zenon_or_s _ _ zenon_H1ba); [ zenon_intro zenon_H29 | zenon_intro zenon_H179 ]. % 4.69/4.91 apply (zenon_L260_); trivial. % 4.69/4.91 apply (zenon_L303_); trivial. % 4.69/4.91 (* end of lemma zenon_L304_ *) % 4.69/4.91 assert (zenon_L305_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> False). % 4.69/4.91 do 0 intro. intros zenon_H118 zenon_H5b zenon_Hb9 zenon_H135 zenon_H132 zenon_H36 zenon_H7c zenon_H7b zenon_H1c7 zenon_H1ab zenon_H34 zenon_H25 zenon_Hd0 zenon_H4b zenon_H179 zenon_H16c zenon_H4c. % 4.69/4.91 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H5a | zenon_intro zenon_H119 ]. % 4.69/4.91 exact (zenon_H5b zenon_H5a). % 4.69/4.91 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H9c | zenon_intro zenon_H11c ]. % 4.69/4.91 apply (zenon_L92_); trivial. % 4.69/4.91 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H87 ]. % 4.69/4.91 apply (zenon_L88_); trivial. % 4.69/4.91 apply (zenon_L269_); trivial. % 4.69/4.91 (* end of lemma zenon_L305_ *) % 4.69/4.91 assert (zenon_L306_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 4.69/4.91 do 0 intro. intros zenon_H137 zenon_H5b zenon_H7c zenon_Hb9 zenon_H42 zenon_H103 zenon_H104 zenon_H2c zenon_H2b zenon_H198 zenon_H29 zenon_H28 zenon_Hf6 zenon_H16c zenon_H195 zenon_H194 zenon_H87 zenon_H13c. % 4.69/4.91 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_H5a | zenon_intro zenon_H138 ]. % 4.69/4.91 exact (zenon_H5b zenon_H5a). % 4.69/4.91 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_H7e | zenon_intro zenon_H139 ]. % 4.69/4.91 exact (zenon_H7c zenon_H7e). % 4.69/4.91 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H123 ]. % 4.69/4.91 apply (zenon_L100_); trivial. % 4.69/4.91 apply (zenon_L156_); trivial. % 4.69/4.91 (* end of lemma zenon_L306_ *) % 4.69/4.91 assert (zenon_L307_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> False). % 4.69/4.91 do 0 intro. intros zenon_H118 zenon_H25 zenon_H135 zenon_H132 zenon_H36 zenon_H7b zenon_H137 zenon_H5b zenon_H7c zenon_Hb9 zenon_H42 zenon_H103 zenon_H104 zenon_H2c zenon_H2b zenon_H198 zenon_H29 zenon_H28 zenon_Hf6 zenon_H16c zenon_H195 zenon_H194 zenon_H13c. % 4.69/4.91 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H5a | zenon_intro zenon_H119 ]. % 4.69/4.91 exact (zenon_H5b zenon_H5a). % 4.69/4.91 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H9c | zenon_intro zenon_H11c ]. % 4.69/4.91 apply (zenon_L92_); trivial. % 4.69/4.91 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H87 ]. % 4.69/4.91 apply (zenon_L88_); trivial. % 4.69/4.91 apply (zenon_L306_); trivial. % 4.69/4.91 (* end of lemma zenon_L307_ *) % 4.69/4.91 assert (zenon_L308_ : ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((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 (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((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) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (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)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> False). % 4.69/4.91 do 0 intro. intros zenon_H19a zenon_H1d zenon_H21 zenon_H20 zenon_H118 zenon_H1ab zenon_Hd0 zenon_H179 zenon_H4b zenon_H4c zenon_H1c7 zenon_H100 zenon_H145 zenon_H140 zenon_H6c zenon_H75 zenon_H9d zenon_H82 zenon_H104 zenon_H54 zenon_H13c zenon_H166 zenon_H86 zenon_H38 zenon_H103 zenon_H13e zenon_Hdf zenon_H7b zenon_H135 zenon_H195 zenon_H36 zenon_Hfd zenon_Hc3 zenon_H19d zenon_H33 zenon_H194 zenon_Hf6 zenon_H16c zenon_H137 zenon_Hb9 zenon_H5b zenon_H89 zenon_H16b zenon_H101 zenon_Haf zenon_H85 zenon_H94 zenon_H28 zenon_H1e1 zenon_H1e2 zenon_H114 zenon_H1e zenon_H1b6 zenon_H122 zenon_H1e7 zenon_H1bd zenon_H11e zenon_H1cc zenon_H1cb zenon_H172 zenon_He9 zenon_H170 zenon_Hd7 zenon_H1ca zenon_H70 zenon_H142 zenon_H117 zenon_H152 zenon_H173 zenon_H165 zenon_H171 zenon_H113 zenon_H12e zenon_Hb3 zenon_H132 zenon_Hef zenon_H11f zenon_H153 zenon_H1c0 zenon_H177 zenon_H174 zenon_H176 zenon_H175 zenon_H1c5. % 4.69/4.91 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H2b | zenon_intro zenon_Hb4 ]. % 4.69/4.91 apply (zenon_L300_); trivial. % 4.69/4.91 apply (zenon_L293_); trivial. % 4.69/4.91 (* end of lemma zenon_L308_ *) % 4.69/4.91 assert (zenon_L309_ : ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((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)) = (e0))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (((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))))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (e1))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (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))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> False). % 4.69/4.92 do 0 intro. intros zenon_H1b9 zenon_H175 zenon_H176 zenon_H174 zenon_H177 zenon_H1c0 zenon_H1bd zenon_H1e7 zenon_H122 zenon_H1b6 zenon_H1e2 zenon_H1e1 zenon_Haf zenon_H16b zenon_H89 zenon_H33 zenon_H19d zenon_Hc3 zenon_H38 zenon_H86 zenon_H166 zenon_H1c5 zenon_H18f zenon_H82 zenon_H9d zenon_Hfd zenon_H100 zenon_H186 zenon_H1c4 zenon_H1e zenon_H114 zenon_H101 zenon_H54 zenon_Hef zenon_H137 zenon_H104 zenon_H28 zenon_H198 zenon_H194 zenon_Hf6 zenon_H195 zenon_H13c zenon_H103 zenon_H5b zenon_Hb9 zenon_H7b zenon_H135 zenon_H132 zenon_H36 zenon_H7c zenon_H1c7 zenon_H16c zenon_H4c zenon_H4b zenon_H179 zenon_Hd0 zenon_H1ab zenon_H118 zenon_H20 zenon_H21 zenon_H1d zenon_H11e zenon_H1cc zenon_H1cb zenon_H172 zenon_He9 zenon_H170 zenon_Hd7 zenon_H1ca zenon_H94 zenon_H75 zenon_H70 zenon_H142 zenon_H117 zenon_H152 zenon_H6c zenon_H173 zenon_H165 zenon_H171 zenon_H13e zenon_H140 zenon_Hdf zenon_H95 zenon_H85 zenon_H113 zenon_H12e zenon_Hb3 zenon_H11f zenon_H153 zenon_H19a. % 4.69/4.92 apply (zenon_or_s _ _ zenon_H1b9); [ zenon_intro zenon_H29 | zenon_intro zenon_H145 ]. % 4.69/4.92 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H2b | zenon_intro zenon_Hb4 ]. % 4.69/4.92 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H2c | zenon_intro zenon_H4d ]. % 4.69/4.92 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ]. % 4.69/4.92 exact (zenon_H1e zenon_H23). % 4.69/4.92 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ]. % 4.69/4.92 apply (zenon_or_s _ _ zenon_H114); [ zenon_intro zenon_H23 | zenon_intro zenon_H115 ]. % 4.69/4.92 exact (zenon_H1e zenon_H23). % 4.69/4.92 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H34 | zenon_intro zenon_H116 ]. % 4.69/4.92 apply (zenon_L305_); trivial. % 4.69/4.92 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H42 | zenon_intro zenon_Hbd ]. % 4.69/4.92 apply (zenon_L307_); trivial. % 4.69/4.92 apply (zenon_L236_); trivial. % 4.69/4.92 apply (zenon_or_s _ _ zenon_H24); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 4.69/4.92 exact (zenon_H20 zenon_H27). % 4.69/4.92 exact (zenon_H21 zenon_H26). % 4.69/4.92 apply (zenon_L228_); trivial. % 4.69/4.92 apply (zenon_L259_); trivial. % 4.69/4.92 apply (zenon_L308_); trivial. % 4.69/4.92 (* end of lemma zenon_L309_ *) % 4.69/4.92 assert (zenon_L310_ : ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> (((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 (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((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 (e2) (e2)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((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 (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> False). % 4.69/4.92 do 0 intro. intros zenon_H1ba zenon_H166 zenon_H86 zenon_H38 zenon_Hc3 zenon_H19d zenon_H33 zenon_H89 zenon_H16b zenon_Haf zenon_H1e1 zenon_H1e2 zenon_H1b6 zenon_H122 zenon_H1e7 zenon_H1bd zenon_H1c0 zenon_H177 zenon_H174 zenon_H176 zenon_H175 zenon_H1b9 zenon_H1c5 zenon_H18f zenon_H82 zenon_H9d zenon_Hfd zenon_H54 zenon_H100 zenon_H4b zenon_H4c zenon_H186 zenon_H1c4 zenon_H1e zenon_H118 zenon_H101 zenon_H13c zenon_H28 zenon_Hef zenon_H103 zenon_H195 zenon_H16c zenon_Hf6 zenon_H194 zenon_H198 zenon_H104 zenon_H137 zenon_H7c zenon_H36 zenon_H132 zenon_H135 zenon_H7b zenon_Hb9 zenon_H5b zenon_H20 zenon_H21 zenon_H1d zenon_H11e zenon_H1cc zenon_H1cb zenon_H172 zenon_He9 zenon_H1ab zenon_H170 zenon_H1c7 zenon_Hd7 zenon_H1ca zenon_H94 zenon_Hd0 zenon_H75 zenon_H70 zenon_H142 zenon_H117 zenon_H152 zenon_H6c zenon_H173 zenon_H165 zenon_H171 zenon_H13e zenon_H140 zenon_Hdf zenon_H95 zenon_H85 zenon_H113 zenon_H12e zenon_Hb3 zenon_H114 zenon_H11f zenon_H153 zenon_H19a. % 4.69/4.92 apply (zenon_or_s _ _ zenon_H1ba); [ zenon_intro zenon_H29 | zenon_intro zenon_H179 ]. % 4.69/4.92 apply (zenon_L260_); trivial. % 4.69/4.92 apply (zenon_L309_); trivial. % 4.69/4.92 (* end of lemma zenon_L310_ *) % 4.69/4.92 assert (zenon_L311_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 4.69/4.92 do 0 intro. intros zenon_H103 zenon_H104 zenon_H2c zenon_H2b zenon_H198 zenon_H29 zenon_H28 zenon_H13c zenon_Hb8 zenon_H26 zenon_H54. % 4.69/4.92 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_H108 | zenon_intro zenon_H107 ]. % 4.69/4.92 exact (zenon_H104 zenon_H108). % 4.69/4.92 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H109 ]. % 4.69/4.92 apply (zenon_L155_); trivial. % 4.69/4.92 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Hed | zenon_intro zenon_H8c ]. % 4.69/4.92 apply (zenon_L144_); trivial. % 4.69/4.92 apply (zenon_L60_); trivial. % 4.69/4.92 (* end of lemma zenon_L311_ *) % 4.69/4.92 assert (zenon_L312_ : (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e0)) -> ((op (e2) (e2)) = (e0)) -> False). % 4.69/4.92 do 0 intro. intros zenon_H46 zenon_He5 zenon_H43. % 4.69/4.92 cut (((op (e1) (e2)) = (e0)) = ((op (e1) (e2)) = (op (e2) (e2)))). % 4.69/4.92 intro zenon_D_pnotp. % 4.69/4.92 apply zenon_H46. % 4.69/4.92 rewrite <- zenon_D_pnotp. % 4.69/4.92 exact zenon_He5. % 4.69/4.92 cut (((e0) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H44]. % 4.69/4.92 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 4.69/4.92 congruence. % 4.69/4.92 apply zenon_H4a. apply refl_equal. % 4.69/4.92 apply zenon_H44. apply sym_equal. exact zenon_H43. % 4.69/4.92 (* end of lemma zenon_L312_ *) % 4.69/4.92 assert (zenon_L313_ : (((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). % 4.69/4.92 do 0 intro. intros zenon_H4b zenon_He5 zenon_H46 zenon_H16c zenon_H4c zenon_H4d. % 4.69/4.92 apply (zenon_or_s _ _ zenon_H4b); [ zenon_intro zenon_H43 | zenon_intro zenon_H4e ]. % 4.69/4.92 apply (zenon_L312_); trivial. % 4.69/4.92 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H48 | zenon_intro zenon_H4f ]. % 4.69/4.92 exact (zenon_H16c zenon_H48). % 4.69/4.92 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H51 | zenon_intro zenon_H50 ]. % 4.69/4.92 exact (zenon_H4c zenon_H51). % 4.69/4.92 exact (zenon_H4d zenon_H50). % 4.69/4.92 (* end of lemma zenon_L313_ *) % 4.69/4.92 assert (zenon_L314_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (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). % 4.69/4.92 do 0 intro. intros zenon_He9 zenon_Hbe zenon_Hbd zenon_Hc3 zenon_H4d zenon_H4c zenon_H16c zenon_H46 zenon_H4b zenon_H86 zenon_H26. % 4.69/4.92 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H34 | zenon_intro zenon_Hea ]. % 4.69/4.92 apply (zenon_L36_); trivial. % 4.69/4.92 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H3a | zenon_intro zenon_Heb ]. % 4.69/4.92 exact (zenon_Hc3 zenon_H3a). % 4.69/4.92 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_He5 | zenon_intro zenon_H7a ]. % 4.69/4.92 apply (zenon_L313_); trivial. % 4.69/4.92 apply (zenon_L42_); trivial. % 4.69/4.92 (* end of lemma zenon_L314_ *) % 4.69/4.92 assert (zenon_L315_ : ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((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 (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (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 (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> False). % 4.69/4.92 do 0 intro. intros zenon_H1ba zenon_H1d zenon_H1e9 zenon_H6c zenon_H140 zenon_H113 zenon_H75 zenon_Hbe zenon_H4b zenon_H4c zenon_H46 zenon_H86 zenon_He9 zenon_H20 zenon_H5b zenon_Hb9 zenon_H137 zenon_H18f zenon_H4d zenon_H33 zenon_H38 zenon_H19d zenon_Hc3 zenon_H9d zenon_H103 zenon_Hfd zenon_H195 zenon_H16c zenon_Hf6 zenon_H194 zenon_H54 zenon_H104 zenon_H100 zenon_H36 zenon_Hef zenon_H28 zenon_H2c zenon_H13c zenon_H101 zenon_H7c zenon_H198 zenon_H118 zenon_H1e zenon_H175 zenon_H176 zenon_H174 zenon_H177 zenon_H1c0 zenon_H153 zenon_H11f zenon_H114 zenon_H7b zenon_H132 zenon_H82 zenon_Hb3 zenon_H12e zenon_Hdf zenon_H13e zenon_H171 zenon_H165 zenon_H173 zenon_H152 zenon_H117 zenon_H142 zenon_H70 zenon_Hd0 zenon_H94 zenon_H1ca zenon_Hd7 zenon_H1c7 zenon_H170 zenon_H1ab zenon_H172 zenon_H1cb zenon_H1cc zenon_H11e zenon_H1bd zenon_H1e7 zenon_H122 zenon_H19a. % 4.69/4.92 apply (zenon_or_s _ _ zenon_H1ba); [ zenon_intro zenon_H29 | zenon_intro zenon_H179 ]. % 4.69/4.92 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H2b | zenon_intro zenon_Hb4 ]. % 4.69/4.92 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ]. % 4.69/4.92 exact (zenon_H1e zenon_H23). % 4.69/4.92 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ]. % 4.69/4.92 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H5a | zenon_intro zenon_H119 ]. % 4.69/4.92 exact (zenon_H5b zenon_H5a). % 4.69/4.92 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H9c | zenon_intro zenon_H11c ]. % 4.69/4.92 apply (zenon_L92_); trivial. % 4.69/4.92 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H87 ]. % 4.69/4.92 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_H5a | zenon_intro zenon_H138 ]. % 4.69/4.92 exact (zenon_H5b zenon_H5a). % 4.69/4.92 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_H7e | zenon_intro zenon_H139 ]. % 4.69/4.92 exact (zenon_H7c zenon_H7e). % 4.69/4.92 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H123 ]. % 4.69/4.92 apply (zenon_L154_); trivial. % 4.69/4.92 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hb6 | zenon_intro zenon_H105 ]. % 4.69/4.92 apply (zenon_L147_); trivial. % 4.69/4.92 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H5e | zenon_intro zenon_H106 ]. % 4.69/4.92 apply (zenon_L164_); trivial. % 4.69/4.92 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_H92 | zenon_intro zenon_H8a ]. % 4.69/4.92 apply (zenon_L149_); trivial. % 4.69/4.92 apply (zenon_L152_); trivial. % 4.69/4.92 apply (zenon_L157_); trivial. % 4.69/4.92 apply (zenon_or_s _ _ zenon_H24); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 4.69/4.92 exact (zenon_H20 zenon_H27). % 4.69/4.92 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H196 ]. % 4.69/4.92 apply (zenon_L311_); trivial. % 4.69/4.92 apply (zenon_or_s _ _ zenon_H196); [ zenon_intro zenon_H47 | zenon_intro zenon_H197 ]. % 4.69/4.92 exact (zenon_H195 zenon_H47). % 4.69/4.92 apply (zenon_or_s _ _ zenon_H197); [ zenon_intro zenon_H48 | zenon_intro zenon_H192 ]. % 4.69/4.92 exact (zenon_H16c zenon_H48). % 4.69/4.92 apply (zenon_or_s _ _ zenon_H1e9); [ zenon_intro zenon_Hbd | zenon_intro zenon_H1ea ]. % 4.69/4.92 apply (zenon_L314_); trivial. % 4.69/4.92 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_H123 | zenon_intro zenon_H1eb ]. % 4.69/4.92 apply (zenon_L150_); trivial. % 4.69/4.92 apply (zenon_or_s _ _ zenon_H1eb); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H2e ]. % 4.69/4.92 apply (zenon_or_s _ _ zenon_H75); [ zenon_intro zenon_H6d | zenon_intro zenon_H77 ]. % 4.69/4.92 apply (zenon_L13_); trivial. % 4.69/4.92 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H72 | zenon_intro zenon_H78 ]. % 4.69/4.92 exact (zenon_H140 zenon_H72). % 4.69/4.92 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H79 | zenon_intro zenon_H31 ]. % 4.69/4.92 apply (zenon_L230_); trivial. % 4.69/4.92 exact (zenon_H2c zenon_H31). % 4.69/4.92 exact (zenon_H29 zenon_H2e). % 4.69/4.92 apply (zenon_L298_); trivial. % 4.69/4.92 apply (zenon_L193_); trivial. % 4.69/4.92 (* end of lemma zenon_L315_ *) % 4.69/4.92 assert (zenon_L316_ : ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e2) (e0)) = (op (e2) (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 (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((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 (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (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) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (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)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> False). % 4.69/4.92 do 0 intro. intros zenon_H1bb zenon_H122 zenon_H1e7 zenon_H1bd zenon_H11e zenon_H1cc zenon_H1cb zenon_H172 zenon_H1ab zenon_H170 zenon_H1c7 zenon_Hd7 zenon_H1ca zenon_H94 zenon_Hd0 zenon_H70 zenon_H142 zenon_H117 zenon_H152 zenon_H173 zenon_H165 zenon_H171 zenon_H13e zenon_Hdf zenon_H12e zenon_Hb3 zenon_H132 zenon_H7b zenon_H114 zenon_H153 zenon_H1c0 zenon_H177 zenon_H174 zenon_H176 zenon_H175 zenon_H19d zenon_H38 zenon_H33 zenon_He9 zenon_H86 zenon_H46 zenon_Hbe zenon_H75 zenon_H113 zenon_H140 zenon_H6c zenon_H1e9 zenon_H1ba zenon_H1d zenon_H20 zenon_H5b zenon_Hb9 zenon_H137 zenon_H18f zenon_H82 zenon_H9d zenon_H103 zenon_Hfd zenon_H195 zenon_Hf6 zenon_H194 zenon_H54 zenon_H100 zenon_H104 zenon_H4b zenon_H4d zenon_H4c zenon_H16c zenon_H13c zenon_H186 zenon_H7c zenon_H198 zenon_H36 zenon_Hef zenon_H28 zenon_H2c zenon_H101 zenon_H118 zenon_H1e zenon_H11f zenon_H19a. % 4.69/4.92 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H29 | zenon_intro zenon_Hc3 ]. % 4.69/4.92 apply (zenon_L160_); trivial. % 4.69/4.92 apply (zenon_L315_); trivial. % 4.69/4.92 (* end of lemma zenon_L316_ *) % 4.69/4.92 assert (zenon_L317_ : ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (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 (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> False). % 4.69/4.92 do 0 intro. intros zenon_H1ec zenon_H1e9 zenon_Hbe zenon_H46 zenon_H86 zenon_H33 zenon_H38 zenon_H19d zenon_H175 zenon_H176 zenon_H174 zenon_H177 zenon_H1c0 zenon_H1bd zenon_H1e7 zenon_H122 zenon_H1bb zenon_H19a zenon_H153 zenon_H11f zenon_H114 zenon_H7b zenon_H135 zenon_H132 zenon_Hb3 zenon_H12e zenon_H113 zenon_H95 zenon_Hdf zenon_H140 zenon_H13e zenon_H21 zenon_H171 zenon_H165 zenon_H173 zenon_H6c zenon_H152 zenon_H117 zenon_H142 zenon_H70 zenon_H75 zenon_Hd0 zenon_H94 zenon_H1ca zenon_Hd7 zenon_H1c7 zenon_H170 zenon_H1ab zenon_He9 zenon_H172 zenon_H1cb zenon_H1cc zenon_H11e zenon_H1d zenon_H20 zenon_H5b zenon_Hb9 zenon_H137 zenon_H18f zenon_H82 zenon_H9d zenon_H103 zenon_Hfd zenon_H195 zenon_Hf6 zenon_H194 zenon_H54 zenon_H100 zenon_H104 zenon_H4b zenon_H4d zenon_H4c zenon_H16c zenon_H13c zenon_H186 zenon_H7c zenon_H198 zenon_H36 zenon_Hef zenon_H28 zenon_H101 zenon_H118 zenon_H1e zenon_H1c4 zenon_H1ba. % 4.69/4.92 apply (zenon_or_s _ _ zenon_H1ec); [ zenon_intro zenon_H85 | zenon_intro zenon_H2c ]. % 4.69/4.92 apply (zenon_or_s _ _ zenon_H1ba); [ zenon_intro zenon_H29 | zenon_intro zenon_H179 ]. % 4.69/4.92 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H2b | zenon_intro zenon_Hb4 ]. % 4.69/4.92 apply (zenon_L228_); trivial. % 4.69/4.92 apply (zenon_L259_); trivial. % 4.69/4.92 apply (zenon_L193_); trivial. % 4.69/4.92 apply (zenon_L316_); trivial. % 4.69/4.92 (* end of lemma zenon_L317_ *) % 4.69/4.92 assert (zenon_L318_ : ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (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 (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> (((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) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> False). % 4.69/4.92 do 0 intro. intros zenon_H1ed zenon_H46 zenon_Hbe zenon_H1e9 zenon_H1ec zenon_H19a zenon_H153 zenon_H11f zenon_H114 zenon_Hb3 zenon_H12e zenon_H113 zenon_H95 zenon_Hdf zenon_H140 zenon_H13e zenon_H171 zenon_H165 zenon_H173 zenon_H6c zenon_H152 zenon_H117 zenon_H142 zenon_H70 zenon_H75 zenon_Hd0 zenon_H94 zenon_H1ca zenon_Hd7 zenon_H1c7 zenon_H170 zenon_H1ab zenon_He9 zenon_H172 zenon_H1cb zenon_H1cc zenon_H11e zenon_H1d zenon_H21 zenon_H20 zenon_H5b zenon_Hb9 zenon_H7b zenon_H135 zenon_H132 zenon_H36 zenon_H7c zenon_H137 zenon_H104 zenon_H198 zenon_H194 zenon_Hf6 zenon_H16c zenon_H195 zenon_H103 zenon_Hef zenon_H28 zenon_H13c zenon_H101 zenon_H118 zenon_H1e zenon_H1c4 zenon_H186 zenon_H4c zenon_H4b zenon_H100 zenon_H54 zenon_Hfd zenon_H9d zenon_H82 zenon_H18f zenon_H1c5 zenon_H1ba zenon_H166 zenon_H86 zenon_H38 zenon_H19d zenon_H33 zenon_H89 zenon_H16b zenon_Haf zenon_H1e1 zenon_H1e2 zenon_H1b6 zenon_H122 zenon_H1e7 zenon_H1bd zenon_H1c0 zenon_H177 zenon_H174 zenon_H176 zenon_H175 zenon_H1b9 zenon_H1bb. % 4.69/4.92 apply (zenon_or_s _ _ zenon_H1ed); [ zenon_intro zenon_H85 | zenon_intro zenon_H4d ]. % 4.69/4.92 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H29 | zenon_intro zenon_Hc3 ]. % 4.69/4.92 apply (zenon_L260_); trivial. % 4.69/4.92 apply (zenon_L310_); trivial. % 4.69/4.92 apply (zenon_L317_); trivial. % 4.69/4.92 (* end of lemma zenon_L318_ *) % 4.69/4.92 assert (zenon_L319_ : ((~((op (e2) (e3)) = (e2)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (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 (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> False). % 4.69/4.92 do 0 intro. intros zenon_H1ee zenon_H1ec zenon_H1e9 zenon_H46 zenon_H1ed zenon_H19a zenon_H153 zenon_H11f zenon_H114 zenon_Hb3 zenon_H12e zenon_H113 zenon_H95 zenon_Hdf zenon_H140 zenon_H13e zenon_H171 zenon_H165 zenon_H173 zenon_H6c zenon_H152 zenon_H117 zenon_H142 zenon_H70 zenon_H75 zenon_Hd0 zenon_H94 zenon_H1ca zenon_Hd7 zenon_H1c7 zenon_H170 zenon_H1ab zenon_He9 zenon_H172 zenon_H1cb zenon_H1cc zenon_H11e zenon_H1d zenon_H21 zenon_H20 zenon_H5b zenon_Hb9 zenon_H7b zenon_H135 zenon_H132 zenon_H36 zenon_H7c zenon_H137 zenon_H104 zenon_H198 zenon_H194 zenon_Hf6 zenon_H16c zenon_H195 zenon_H103 zenon_Hef zenon_H28 zenon_H13c zenon_H101 zenon_H118 zenon_H1e zenon_H1c4 zenon_H186 zenon_H4c zenon_H4b zenon_H100 zenon_H54 zenon_Hfd zenon_H9d zenon_H82 zenon_H18f zenon_H1c5 zenon_H1ba zenon_Hbe zenon_H1de zenon_H89 zenon_H16b zenon_H1e1 zenon_H1e2 zenon_H175 zenon_H176 zenon_H174 zenon_H177 zenon_H1c0 zenon_H1bd zenon_H1e7 zenon_H122 zenon_H1b6 zenon_Haf zenon_H33 zenon_H19d zenon_H86 zenon_H166 zenon_H1e8 zenon_H1b9 zenon_H1bb. % 4.69/4.92 apply (zenon_or_s _ _ zenon_H1ee); [ zenon_intro zenon_H85 | zenon_intro zenon_H38 ]. % 4.69/4.92 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H29 | zenon_intro zenon_Hc3 ]. % 4.69/4.92 apply (zenon_L260_); trivial. % 4.69/4.92 apply (zenon_L304_); trivial. % 4.69/4.92 apply (zenon_L318_); trivial. % 4.69/4.92 (* end of lemma zenon_L319_ *) % 4.69/4.92 assert (zenon_L320_ : ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (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 (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((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)) = (e0))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> False). % 4.69/4.92 do 0 intro. intros zenon_H1ed zenon_H1bb zenon_H46 zenon_Hbe zenon_H1e9 zenon_H1ec zenon_H19a zenon_H153 zenon_H11f zenon_H114 zenon_Hb3 zenon_H12e zenon_H113 zenon_H95 zenon_Hdf zenon_H140 zenon_H13e zenon_H171 zenon_H165 zenon_H173 zenon_H6c zenon_H152 zenon_H117 zenon_H142 zenon_H70 zenon_H75 zenon_Hd0 zenon_H94 zenon_H1ca zenon_Hd7 zenon_H1c7 zenon_H170 zenon_H1ab zenon_He9 zenon_H172 zenon_H1cb zenon_H1cc zenon_H11e zenon_H1d zenon_H21 zenon_H20 zenon_H5b zenon_Hb9 zenon_H7b zenon_H135 zenon_H132 zenon_H36 zenon_H7c zenon_H137 zenon_H104 zenon_H198 zenon_H194 zenon_Hf6 zenon_H16c zenon_H195 zenon_H103 zenon_Hef zenon_H28 zenon_H13c zenon_H101 zenon_H118 zenon_H1e zenon_H1c4 zenon_H186 zenon_H4c zenon_H4b zenon_H100 zenon_H54 zenon_Hfd zenon_H9d zenon_H82 zenon_H18f zenon_H1c5 zenon_H1b9 zenon_H175 zenon_H176 zenon_H174 zenon_H177 zenon_H1c0 zenon_H1bd zenon_H1e7 zenon_H122 zenon_H1b6 zenon_H1e2 zenon_H1e1 zenon_Haf zenon_H16b zenon_H89 zenon_H33 zenon_H19d zenon_Hc3 zenon_H38 zenon_H86 zenon_H166 zenon_H1ba. % 4.69/4.92 apply (zenon_or_s _ _ zenon_H1ed); [ zenon_intro zenon_H85 | zenon_intro zenon_H4d ]. % 4.69/4.92 apply (zenon_L310_); trivial. % 4.69/4.92 apply (zenon_L317_); trivial. % 4.69/4.92 (* end of lemma zenon_L320_ *) % 4.69/4.92 assert (zenon_L321_ : ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (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 (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (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 (e1) (e1)) = (e0))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> False). % 4.69/4.92 do 0 intro. intros zenon_H1ed zenon_H1c5 zenon_H175 zenon_H176 zenon_H174 zenon_H177 zenon_H1c0 zenon_H153 zenon_H11f zenon_Hef zenon_H132 zenon_Hb3 zenon_H12e zenon_H113 zenon_H171 zenon_H165 zenon_H173 zenon_H152 zenon_H117 zenon_H142 zenon_H70 zenon_H1ca zenon_Hd7 zenon_H170 zenon_He9 zenon_H172 zenon_H1cb zenon_H1cc zenon_H11e zenon_H1bd zenon_H1e7 zenon_H122 zenon_H1b6 zenon_H1e zenon_H114 zenon_H1e2 zenon_H1e1 zenon_H28 zenon_H94 zenon_Haf zenon_H101 zenon_H16b zenon_H89 zenon_H5b zenon_Hb9 zenon_H137 zenon_H16c zenon_Hf6 zenon_H194 zenon_H33 zenon_H19d zenon_Hc3 zenon_Hfd zenon_H36 zenon_H195 zenon_H135 zenon_H7b zenon_Hdf zenon_H13e zenon_H103 zenon_H38 zenon_H86 zenon_H166 zenon_H13c zenon_H54 zenon_H104 zenon_H82 zenon_H9d zenon_H75 zenon_H6c zenon_H140 zenon_H145 zenon_H100 zenon_H1c7 zenon_H4c zenon_H4b zenon_H179 zenon_Hd0 zenon_H1ab zenon_H118 zenon_H20 zenon_H21 zenon_H1d zenon_H19a. % 4.69/4.92 apply (zenon_or_s _ _ zenon_H1ed); [ zenon_intro zenon_H85 | zenon_intro zenon_H4d ]. % 4.69/4.92 apply (zenon_L308_); trivial. % 4.69/4.92 apply (zenon_L193_); trivial. % 4.69/4.92 (* end of lemma zenon_L321_ *) % 4.69/4.92 assert (zenon_L322_ : ((~((op (e2) (e3)) = (e2)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (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))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> False). % 4.69/4.93 do 0 intro. intros zenon_H1ee zenon_H1ed zenon_H1e8 zenon_H100 zenon_H6c zenon_H104 zenon_H166 zenon_H86 zenon_H103 zenon_H13e zenon_Hdf zenon_H7b zenon_H135 zenon_H195 zenon_Hfd zenon_Hc3 zenon_H19d zenon_H33 zenon_H194 zenon_Hf6 zenon_H137 zenon_Haf zenon_H1b6 zenon_H122 zenon_H1e7 zenon_H1bd zenon_H11e zenon_H1cc zenon_H1cb zenon_H172 zenon_He9 zenon_H170 zenon_Hd7 zenon_H1ca zenon_H70 zenon_H142 zenon_H117 zenon_H152 zenon_H173 zenon_H165 zenon_H171 zenon_H113 zenon_H12e zenon_Hb3 zenon_H132 zenon_Hef zenon_H11f zenon_H153 zenon_H1c0 zenon_H177 zenon_H174 zenon_H176 zenon_H175 zenon_H1c5 zenon_H1e zenon_H114 zenon_H1e2 zenon_H1e1 zenon_H101 zenon_H28 zenon_H13c zenon_H54 zenon_H82 zenon_H9d zenon_H94 zenon_H36 zenon_H16b zenon_H89 zenon_H5b zenon_Hb9 zenon_H1de zenon_H145 zenon_H140 zenon_H75 zenon_H198 zenon_Hbe zenon_H1c7 zenon_H16c zenon_H4c zenon_H4b zenon_H179 zenon_Hd0 zenon_H1ab zenon_H118 zenon_H20 zenon_H21 zenon_H1d zenon_H19a. % 4.69/4.93 apply (zenon_or_s _ _ zenon_H1ee); [ zenon_intro zenon_H85 | zenon_intro zenon_H38 ]. % 4.69/4.93 apply (zenon_L302_); trivial. % 4.69/4.93 apply (zenon_L321_); trivial. % 4.69/4.93 (* end of lemma zenon_L322_ *) % 4.69/4.93 assert (zenon_L323_ : ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (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 (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (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 (e1) (e1)) = (e0))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> False). % 4.69/4.93 do 0 intro. intros zenon_H1ef zenon_H1ed zenon_H1c5 zenon_H175 zenon_H176 zenon_H174 zenon_H177 zenon_H1c0 zenon_H153 zenon_H11f zenon_Hef zenon_H132 zenon_Hb3 zenon_H12e zenon_H113 zenon_H171 zenon_H165 zenon_H173 zenon_H152 zenon_H117 zenon_H142 zenon_H70 zenon_H1ca zenon_Hd7 zenon_H170 zenon_He9 zenon_H172 zenon_H1cb zenon_H1cc zenon_H11e zenon_H1bd zenon_H1e7 zenon_H122 zenon_H1b6 zenon_H1e zenon_H114 zenon_H1e2 zenon_H1e1 zenon_H28 zenon_H94 zenon_Haf zenon_H101 zenon_H16b zenon_H89 zenon_H5b zenon_Hb9 zenon_H137 zenon_H16c zenon_Hf6 zenon_H194 zenon_H33 zenon_H19d zenon_Hc3 zenon_Hfd zenon_H36 zenon_H195 zenon_H7b zenon_Hdf zenon_H13e zenon_H103 zenon_H38 zenon_H86 zenon_H166 zenon_H13c zenon_H54 zenon_H104 zenon_H82 zenon_H9d zenon_H75 zenon_H6c zenon_H140 zenon_H145 zenon_H100 zenon_H1c7 zenon_H4b zenon_H179 zenon_Hd0 zenon_H1ab zenon_H118 zenon_H20 zenon_H21 zenon_H1d zenon_H19a. % 4.69/4.93 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H135 | zenon_intro zenon_H4d ]. % 4.69/4.93 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H4c | zenon_intro zenon_Hb4 ]. % 4.69/4.93 apply (zenon_L321_); trivial. % 4.69/4.93 apply (zenon_L294_); trivial. % 4.69/4.93 apply (zenon_L299_); trivial. % 4.69/4.93 (* end of lemma zenon_L323_ *) % 4.69/4.93 assert (zenon_L324_ : ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (e1))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> False). % 4.69/4.93 do 0 intro. intros zenon_H1f0 zenon_H1ef zenon_H1ee zenon_H1ed zenon_H1e8 zenon_H100 zenon_H6c zenon_H104 zenon_H166 zenon_H86 zenon_H103 zenon_H13e zenon_Hdf zenon_H7b zenon_H195 zenon_Hfd zenon_Hc3 zenon_H19d zenon_H33 zenon_H194 zenon_Hf6 zenon_H137 zenon_Haf zenon_H1b6 zenon_H122 zenon_H1e7 zenon_H1bd zenon_H11e zenon_H1cc zenon_H1cb zenon_H172 zenon_He9 zenon_H170 zenon_Hd7 zenon_H1ca zenon_H70 zenon_H142 zenon_H117 zenon_H152 zenon_H173 zenon_H165 zenon_H171 zenon_H113 zenon_H12e zenon_Hb3 zenon_H132 zenon_Hef zenon_H11f zenon_H153 zenon_H1c0 zenon_H177 zenon_H174 zenon_H176 zenon_H175 zenon_H1c5 zenon_H1e zenon_H114 zenon_H1e2 zenon_H1e1 zenon_H101 zenon_H28 zenon_H13c zenon_H54 zenon_H82 zenon_H9d zenon_H94 zenon_H36 zenon_H16b zenon_H89 zenon_H5b zenon_Hb9 zenon_H1de zenon_H145 zenon_H140 zenon_H75 zenon_H198 zenon_Hbe zenon_H1c7 zenon_H16c zenon_H4b zenon_H179 zenon_Hd0 zenon_H1ab zenon_H118 zenon_H20 zenon_H21 zenon_H1d zenon_H19a. % 4.69/4.93 apply (zenon_or_s _ _ zenon_H1f0); [ zenon_intro zenon_H135 | zenon_intro zenon_H38 ]. % 4.69/4.93 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H4c | zenon_intro zenon_Hb4 ]. % 4.69/4.93 apply (zenon_L322_); trivial. % 4.69/4.93 apply (zenon_L294_); trivial. % 4.69/4.93 apply (zenon_L323_); trivial. % 4.69/4.93 (* end of lemma zenon_L324_ *) % 4.69/4.93 assert (zenon_L325_ : ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (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 (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> (~((op (e3) (e0)) = (op (e3) (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)) = (e0))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> False). % 4.69/4.93 do 0 intro. intros zenon_H1ef zenon_H1f0 zenon_H1ee zenon_H1ba zenon_H1ec zenon_H1e9 zenon_H46 zenon_H1bb zenon_H1ed zenon_H19a zenon_H153 zenon_H11f zenon_H114 zenon_Hb3 zenon_H12e zenon_H113 zenon_Hdf zenon_H140 zenon_H13e zenon_H171 zenon_H165 zenon_H173 zenon_H6c zenon_H152 zenon_H117 zenon_H142 zenon_H70 zenon_H75 zenon_Hd0 zenon_H94 zenon_H1ca zenon_Hd7 zenon_H1c7 zenon_H170 zenon_H1ab zenon_He9 zenon_H172 zenon_H1cb zenon_H1cc zenon_H11e zenon_H1d zenon_H21 zenon_H20 zenon_H5b zenon_Hb9 zenon_H7b zenon_H135 zenon_H132 zenon_H36 zenon_H7c zenon_H137 zenon_H104 zenon_H198 zenon_H194 zenon_Hf6 zenon_H16c zenon_H195 zenon_H103 zenon_Hef zenon_H28 zenon_H13c zenon_H101 zenon_H118 zenon_H1e zenon_H1c4 zenon_H186 zenon_H4b zenon_H100 zenon_H54 zenon_Hfd zenon_H9d zenon_H82 zenon_H18f zenon_H1c5 zenon_H179 zenon_Hbe zenon_H1de zenon_H89 zenon_H16b zenon_H1e1 zenon_H1e2 zenon_H175 zenon_H176 zenon_H174 zenon_H177 zenon_H1c0 zenon_H1bd zenon_H1e7 zenon_H122 zenon_H1b6 zenon_Haf zenon_H33 zenon_H19d zenon_Hc3 zenon_H86 zenon_H166 zenon_H1e8 zenon_H1b9. % 4.69/4.93 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H95 | zenon_intro zenon_H145 ]. % 4.69/4.93 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H4c | zenon_intro zenon_Hb4 ]. % 4.69/4.93 apply (zenon_or_s _ _ zenon_H1ee); [ zenon_intro zenon_H85 | zenon_intro zenon_H38 ]. % 4.69/4.93 apply (zenon_L303_); trivial. % 4.69/4.93 apply (zenon_L320_); trivial. % 4.69/4.93 apply (zenon_L287_); trivial. % 4.69/4.93 apply (zenon_L324_); trivial. % 4.69/4.93 (* end of lemma zenon_L325_ *) % 4.69/4.93 assert (zenon_L326_ : ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (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 (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> (((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)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> False). % 4.69/4.93 do 0 intro. intros zenon_H1f0 zenon_H1ef zenon_H1ee zenon_H1ec zenon_H1e9 zenon_H46 zenon_H1bb zenon_H1ed zenon_H19a zenon_H153 zenon_H11f zenon_H114 zenon_Hb3 zenon_H12e zenon_H113 zenon_Hdf zenon_H140 zenon_H13e zenon_H171 zenon_H165 zenon_H173 zenon_H6c zenon_H152 zenon_H117 zenon_H142 zenon_H70 zenon_H75 zenon_Hd0 zenon_H94 zenon_H1ca zenon_Hd7 zenon_H1c7 zenon_H170 zenon_H1ab zenon_He9 zenon_H172 zenon_H1cb zenon_H1cc zenon_H11e zenon_H1d zenon_H21 zenon_H20 zenon_H5b zenon_Hb9 zenon_H7b zenon_H135 zenon_H132 zenon_H36 zenon_H7c zenon_H137 zenon_H104 zenon_H198 zenon_H194 zenon_Hf6 zenon_H16c zenon_H195 zenon_H103 zenon_Hef zenon_H28 zenon_H13c zenon_H101 zenon_H118 zenon_H1e zenon_H1c4 zenon_H186 zenon_H4b zenon_H100 zenon_H54 zenon_Hfd zenon_H9d zenon_H82 zenon_H18f zenon_H1c5 zenon_H1b9 zenon_H1e8 zenon_H166 zenon_H86 zenon_Hc3 zenon_H19d zenon_H33 zenon_Haf zenon_H1b6 zenon_H122 zenon_H1e7 zenon_H1bd zenon_H1c0 zenon_H177 zenon_H174 zenon_H176 zenon_H175 zenon_H1e2 zenon_H1e1 zenon_H16b zenon_H89 zenon_H1de zenon_Hbe zenon_H1ba. % 4.69/4.93 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H95 | zenon_intro zenon_H179 ]. % 4.69/4.93 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H4c | zenon_intro zenon_Hb4 ]. % 4.69/4.93 apply (zenon_or_s _ _ zenon_H1ee); [ zenon_intro zenon_H85 | zenon_intro zenon_H38 ]. % 4.69/4.93 apply (zenon_L304_); trivial. % 4.69/4.93 apply (zenon_L320_); trivial. % 4.69/4.93 apply (zenon_L287_); trivial. % 4.69/4.93 apply (zenon_L325_); trivial. % 4.69/4.93 (* end of lemma zenon_L326_ *) % 4.69/4.93 assert (zenon_L327_ : ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e2) (e0)) = (op (e2) (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 (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((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 (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (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) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (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)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> False). % 4.69/4.93 do 0 intro. intros zenon_H1bf zenon_H1bb zenon_H122 zenon_H1e7 zenon_H1bd zenon_H11e zenon_H1cc zenon_H1cb zenon_H172 zenon_H1ab zenon_H170 zenon_H1c7 zenon_Hd7 zenon_H1ca zenon_H94 zenon_Hd0 zenon_H70 zenon_H142 zenon_H117 zenon_H152 zenon_H173 zenon_H165 zenon_H171 zenon_H13e zenon_Hdf zenon_H12e zenon_Hb3 zenon_H132 zenon_H7b zenon_H114 zenon_H153 zenon_H1c0 zenon_H177 zenon_H174 zenon_H176 zenon_H175 zenon_H19d zenon_H38 zenon_H33 zenon_He9 zenon_H86 zenon_H46 zenon_Hbe zenon_H75 zenon_H113 zenon_H140 zenon_H6c zenon_H1e9 zenon_H1ba zenon_H1d zenon_H20 zenon_H5b zenon_Hb9 zenon_H137 zenon_H18f zenon_H82 zenon_H9d zenon_H103 zenon_Hfd zenon_Hf6 zenon_H194 zenon_H54 zenon_H100 zenon_H104 zenon_H4b zenon_H4d zenon_H16c zenon_H13c zenon_H186 zenon_H7c zenon_H198 zenon_H36 zenon_Hef zenon_H28 zenon_H2c zenon_H101 zenon_H118 zenon_H1e zenon_H11f zenon_H19a zenon_H1b6. % 4.69/4.93 apply (zenon_or_s _ _ zenon_H1bf); [ zenon_intro zenon_H195 | zenon_intro zenon_Hb4 ]. % 4.69/4.93 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H4c | zenon_intro zenon_Hb4 ]. % 4.69/4.93 apply (zenon_L316_); trivial. % 4.69/4.93 apply (zenon_L298_); trivial. % 4.69/4.93 apply (zenon_L73_); trivial. % 4.69/4.93 (* end of lemma zenon_L327_ *) % 4.69/4.93 assert (zenon_L328_ : ((~((op (e1) (e3)) = (e1)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (e1))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((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 (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> False). % 4.69/4.93 do 0 intro. intros zenon_H1f1 zenon_H1bf zenon_H1b6 zenon_H1ba zenon_H1c4 zenon_H1e zenon_H118 zenon_H101 zenon_H28 zenon_Hef zenon_H36 zenon_H198 zenon_H7c zenon_H186 zenon_H13c zenon_H16c zenon_H4d zenon_H4b zenon_H104 zenon_H100 zenon_H54 zenon_H194 zenon_Hf6 zenon_H195 zenon_Hfd zenon_H103 zenon_H9d zenon_H82 zenon_H18f zenon_H137 zenon_Hb9 zenon_H5b zenon_H20 zenon_H1d zenon_H11e zenon_H1cc zenon_H1cb zenon_H172 zenon_He9 zenon_H1ab zenon_H170 zenon_H1c7 zenon_Hd7 zenon_H1ca zenon_H94 zenon_Hd0 zenon_H75 zenon_H70 zenon_H142 zenon_H117 zenon_H152 zenon_H6c zenon_H173 zenon_H165 zenon_H171 zenon_H21 zenon_H13e zenon_H140 zenon_Hdf zenon_H113 zenon_H12e zenon_Hb3 zenon_H132 zenon_H7b zenon_H114 zenon_H11f zenon_H153 zenon_H19a zenon_H1bb zenon_H122 zenon_H1e7 zenon_H1bd zenon_H1c0 zenon_H177 zenon_H174 zenon_H176 zenon_H175 zenon_H19d zenon_H38 zenon_H33 zenon_H86 zenon_H46 zenon_Hbe zenon_H1e9 zenon_H1ec. % 4.69/4.93 apply (zenon_or_s _ _ zenon_H1f1); [ zenon_intro zenon_H135 | zenon_intro zenon_H2c ]. % 4.69/4.93 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H95 | zenon_intro zenon_H179 ]. % 4.69/4.93 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H4c | zenon_intro zenon_Hb4 ]. % 4.69/4.93 apply (zenon_L317_); trivial. % 4.69/4.93 apply (zenon_L287_); trivial. % 4.69/4.93 apply (zenon_L299_); trivial. % 4.69/4.93 apply (zenon_L327_); trivial. % 4.69/4.93 (* end of lemma zenon_L328_ *) % 4.69/4.93 assert (zenon_L329_ : ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((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)) = (e0))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (((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))))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (e1))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> False). % 4.69/4.93 do 0 intro. intros zenon_H1ec zenon_H1e9 zenon_Hbe zenon_H46 zenon_H1bb zenon_H1ba zenon_H1bf zenon_H1f1 zenon_H1b9 zenon_H175 zenon_H176 zenon_H174 zenon_H177 zenon_H1c0 zenon_H1bd zenon_H1e7 zenon_H122 zenon_H1b6 zenon_H1e2 zenon_H1e1 zenon_Haf zenon_H16b zenon_H89 zenon_H33 zenon_H19d zenon_Hc3 zenon_H38 zenon_H86 zenon_H166 zenon_H1c5 zenon_H18f zenon_H82 zenon_H9d zenon_Hfd zenon_H100 zenon_H186 zenon_H1c4 zenon_H1e zenon_H114 zenon_H101 zenon_H54 zenon_Hef zenon_H137 zenon_H104 zenon_H28 zenon_H198 zenon_H194 zenon_Hf6 zenon_H195 zenon_H13c zenon_H103 zenon_H5b zenon_Hb9 zenon_H7b zenon_H132 zenon_H36 zenon_H7c zenon_H1c7 zenon_H16c zenon_H4b zenon_H179 zenon_Hd0 zenon_H1ab zenon_H118 zenon_H20 zenon_H21 zenon_H1d zenon_H11e zenon_H1cc zenon_H1cb zenon_H172 zenon_He9 zenon_H170 zenon_Hd7 zenon_H1ca zenon_H94 zenon_H75 zenon_H70 zenon_H142 zenon_H117 zenon_H152 zenon_H6c zenon_H173 zenon_H165 zenon_H171 zenon_H13e zenon_H140 zenon_Hdf zenon_H113 zenon_H12e zenon_Hb3 zenon_H11f zenon_H153 zenon_H19a zenon_H1ed zenon_H1ef. % 4.69/4.93 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H135 | zenon_intro zenon_H4d ]. % 4.69/4.93 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H95 | zenon_intro zenon_H145 ]. % 4.69/4.93 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H4c | zenon_intro zenon_Hb4 ]. % 4.69/4.93 apply (zenon_or_s _ _ zenon_H1ed); [ zenon_intro zenon_H85 | zenon_intro zenon_H4d ]. % 4.69/4.93 apply (zenon_L309_); trivial. % 4.69/4.93 apply (zenon_L193_); trivial. % 4.69/4.93 apply (zenon_L287_); trivial. % 4.69/4.93 apply (zenon_L323_); trivial. % 4.69/4.93 apply (zenon_L328_); trivial. % 4.69/4.93 (* end of lemma zenon_L329_ *) % 4.69/4.93 assert (zenon_L330_ : ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (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 (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((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)) = (e0))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> False). % 4.69/4.93 do 0 intro. intros zenon_H1ef zenon_H1f1 zenon_H1bf zenon_H1ed zenon_H1bb zenon_H46 zenon_Hbe zenon_H1e9 zenon_H1ec zenon_H19a zenon_H153 zenon_H11f zenon_H114 zenon_Hb3 zenon_H12e zenon_H113 zenon_Hdf zenon_H140 zenon_H13e zenon_H171 zenon_H165 zenon_H173 zenon_H6c zenon_H152 zenon_H117 zenon_H142 zenon_H70 zenon_H75 zenon_Hd0 zenon_H94 zenon_H1ca zenon_Hd7 zenon_H1c7 zenon_H170 zenon_H1ab zenon_He9 zenon_H172 zenon_H1cb zenon_H1cc zenon_H11e zenon_H1d zenon_H21 zenon_H20 zenon_H5b zenon_Hb9 zenon_H7b zenon_H135 zenon_H132 zenon_H36 zenon_H7c zenon_H137 zenon_H104 zenon_H198 zenon_H194 zenon_Hf6 zenon_H16c zenon_H195 zenon_H103 zenon_Hef zenon_H28 zenon_H13c zenon_H101 zenon_H118 zenon_H1e zenon_H1c4 zenon_H186 zenon_H4b zenon_H100 zenon_H54 zenon_Hfd zenon_H9d zenon_H82 zenon_H18f zenon_H1c5 zenon_H1b9 zenon_H175 zenon_H176 zenon_H174 zenon_H177 zenon_H1c0 zenon_H1bd zenon_H1e7 zenon_H122 zenon_H1b6 zenon_H1e2 zenon_H1e1 zenon_Haf zenon_H16b zenon_H89 zenon_H33 zenon_H19d zenon_Hc3 zenon_H38 zenon_H86 zenon_H166 zenon_H1ba. % 4.69/4.93 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H95 | zenon_intro zenon_H179 ]. % 4.69/4.93 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H4c | zenon_intro zenon_Hb4 ]. % 4.69/4.93 apply (zenon_L320_); trivial. % 4.69/4.93 apply (zenon_L287_); trivial. % 4.69/4.93 apply (zenon_L329_); trivial. % 4.69/4.93 (* end of lemma zenon_L330_ *) % 4.69/4.93 assert (zenon_L331_ : ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (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 (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> (((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) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> False). % 4.78/4.94 do 0 intro. intros zenon_H1bf zenon_H1f1 zenon_H1ef zenon_H1ed zenon_H46 zenon_Hbe zenon_H1e9 zenon_H1ec zenon_H19a zenon_H153 zenon_H11f zenon_H114 zenon_Hb3 zenon_H12e zenon_H113 zenon_Hdf zenon_H140 zenon_H13e zenon_H171 zenon_H165 zenon_H173 zenon_H6c zenon_H152 zenon_H117 zenon_H142 zenon_H70 zenon_H75 zenon_Hd0 zenon_H94 zenon_H1ca zenon_Hd7 zenon_H1c7 zenon_H170 zenon_H1ab zenon_He9 zenon_H172 zenon_H1cb zenon_H1cc zenon_H11e zenon_H1d zenon_H21 zenon_H20 zenon_H5b zenon_Hb9 zenon_H7b zenon_H132 zenon_H36 zenon_H7c zenon_H137 zenon_H104 zenon_H198 zenon_H194 zenon_Hf6 zenon_H16c zenon_H103 zenon_Hef zenon_H28 zenon_H13c zenon_H101 zenon_H118 zenon_H1e zenon_H1c4 zenon_H186 zenon_H4b zenon_H100 zenon_H54 zenon_Hfd zenon_H9d zenon_H82 zenon_H18f zenon_H1c5 zenon_H1ba zenon_H166 zenon_H86 zenon_H38 zenon_H19d zenon_H33 zenon_H89 zenon_H16b zenon_Haf zenon_H1e1 zenon_H1e2 zenon_H1b6 zenon_H122 zenon_H1e7 zenon_H1bd zenon_H1c0 zenon_H177 zenon_H174 zenon_H176 zenon_H175 zenon_H1b9 zenon_H1bb. % 4.78/4.94 apply (zenon_or_s _ _ zenon_H1bf); [ zenon_intro zenon_H195 | zenon_intro zenon_Hb4 ]. % 4.78/4.94 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H135 | zenon_intro zenon_H4d ]. % 4.78/4.94 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H95 | zenon_intro zenon_Hc3 ]. % 4.78/4.94 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H4c | zenon_intro zenon_Hb4 ]. % 4.78/4.94 apply (zenon_L318_); trivial. % 4.78/4.94 apply (zenon_L287_); trivial. % 4.78/4.94 apply (zenon_L330_); trivial. % 4.78/4.94 apply (zenon_L328_); trivial. % 4.78/4.94 apply (zenon_L291_); trivial. % 4.78/4.94 (* end of lemma zenon_L331_ *) % 4.78/4.94 assert (zenon_L332_ : ((~((op (e1) (e3)) = (e1)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (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) (e0)) = (op (e3) (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((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) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((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 (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> False). % 4.78/4.94 do 0 intro. intros zenon_H1f1 zenon_H1bf zenon_H1bb zenon_H1b9 zenon_H1e8 zenon_H166 zenon_H86 zenon_H19d zenon_H33 zenon_Haf zenon_H1b6 zenon_H122 zenon_H1e7 zenon_H1bd zenon_H1c0 zenon_H177 zenon_H174 zenon_H176 zenon_H175 zenon_H1e2 zenon_H1e1 zenon_H16b zenon_H89 zenon_H1de zenon_Hbe zenon_H1ba zenon_H1c5 zenon_H18f zenon_H82 zenon_H9d zenon_Hfd zenon_H54 zenon_H100 zenon_H4b zenon_H186 zenon_H1c4 zenon_H1e zenon_H118 zenon_H101 zenon_H13c zenon_H28 zenon_Hef zenon_H103 zenon_H195 zenon_H16c zenon_Hf6 zenon_H194 zenon_H198 zenon_H104 zenon_H137 zenon_H7c zenon_H36 zenon_H132 zenon_H7b zenon_Hb9 zenon_H5b zenon_H20 zenon_H21 zenon_H1d zenon_H11e zenon_H1cc zenon_H1cb zenon_H172 zenon_He9 zenon_H1ab zenon_H170 zenon_H1c7 zenon_Hd7 zenon_H1ca zenon_H94 zenon_Hd0 zenon_H75 zenon_H70 zenon_H142 zenon_H117 zenon_H152 zenon_H6c zenon_H173 zenon_H165 zenon_H171 zenon_H13e zenon_H140 zenon_Hdf zenon_H113 zenon_H12e zenon_Hb3 zenon_H114 zenon_H11f zenon_H153 zenon_H19a zenon_H1ed zenon_H46 zenon_H1e9 zenon_H1ec zenon_H1ee zenon_H1f0 zenon_H1ef. % 4.78/4.94 apply (zenon_or_s _ _ zenon_H1f0); [ zenon_intro zenon_H135 | zenon_intro zenon_H38 ]. % 4.78/4.94 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H95 | zenon_intro zenon_Hc3 ]. % 4.78/4.94 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H4c | zenon_intro zenon_Hb4 ]. % 4.78/4.94 apply (zenon_L319_); trivial. % 4.78/4.94 apply (zenon_L287_); trivial. % 4.78/4.94 apply (zenon_L326_); trivial. % 4.78/4.94 apply (zenon_L331_); trivial. % 4.78/4.94 (* end of lemma zenon_L332_ *) % 4.78/4.94 assert (zenon_L333_ : ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (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 (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> (((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)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e3) (e3)) = (e3)))) -> False). % 4.78/4.94 do 0 intro. intros zenon_H1f0 zenon_H1ef zenon_H1ee zenon_H1ec zenon_H1e9 zenon_H46 zenon_H1bb zenon_H1ed zenon_H19a zenon_H153 zenon_H11f zenon_H114 zenon_Hb3 zenon_H12e zenon_H113 zenon_Hdf zenon_H140 zenon_H13e zenon_H171 zenon_H165 zenon_H173 zenon_H6c zenon_H152 zenon_H117 zenon_H142 zenon_H70 zenon_H75 zenon_Hd0 zenon_H94 zenon_H1ca zenon_Hd7 zenon_H1c7 zenon_H170 zenon_H1ab zenon_He9 zenon_H172 zenon_H1cb zenon_H1cc zenon_H11e zenon_H1d zenon_H21 zenon_H20 zenon_H5b zenon_Hb9 zenon_H7b zenon_H132 zenon_H36 zenon_H7c zenon_H137 zenon_H104 zenon_H198 zenon_H194 zenon_Hf6 zenon_H16c zenon_H103 zenon_Hef zenon_H28 zenon_H13c zenon_H101 zenon_H118 zenon_H1e zenon_H1c4 zenon_H186 zenon_H4b zenon_H100 zenon_H54 zenon_Hfd zenon_H9d zenon_H82 zenon_H18f zenon_H1c5 zenon_H1b9 zenon_H1e8 zenon_H166 zenon_H86 zenon_Hc3 zenon_H19d zenon_H33 zenon_Haf zenon_H1b6 zenon_H122 zenon_H1e7 zenon_H1bd zenon_H1c0 zenon_H177 zenon_H174 zenon_H176 zenon_H175 zenon_H1e2 zenon_H1e1 zenon_H16b zenon_H89 zenon_H1de zenon_Hbe zenon_H1ba zenon_H1bf zenon_H1f1. % 4.78/4.94 apply (zenon_or_s _ _ zenon_H1bf); [ zenon_intro zenon_H195 | zenon_intro zenon_Hb4 ]. % 4.78/4.94 apply (zenon_or_s _ _ zenon_H1f0); [ zenon_intro zenon_H135 | zenon_intro zenon_H38 ]. % 4.78/4.94 apply (zenon_L326_); trivial. % 4.78/4.94 apply (zenon_L331_); trivial. % 4.78/4.94 apply (zenon_L291_); trivial. % 4.78/4.94 (* end of lemma zenon_L333_ *) % 4.78/4.94 assert (zenon_L334_ : ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (e2))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((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 (e1) (e1)) = (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> False). % 4.78/4.94 do 0 intro. intros zenon_H19a zenon_H1d zenon_H21 zenon_H20 zenon_H118 zenon_H1ab zenon_Hd0 zenon_H179 zenon_H4b zenon_H4c zenon_H16c zenon_H1c7 zenon_Hbe zenon_H198 zenon_H75 zenon_H140 zenon_H145 zenon_H1de zenon_Hb9 zenon_H5b zenon_H89 zenon_H16b zenon_H36 zenon_H94 zenon_H85 zenon_H9d zenon_H82 zenon_H54 zenon_H13c zenon_H28 zenon_H101 zenon_H1e1 zenon_H1e2 zenon_H114 zenon_H1e zenon_H1e8 zenon_H100 zenon_H6c zenon_H166 zenon_H86 zenon_H103 zenon_H13e zenon_Hdf zenon_H7b zenon_H135 zenon_H195 zenon_Hfd zenon_Hc3 zenon_H19d zenon_H33 zenon_H194 zenon_Hf6 zenon_H137 zenon_Haf zenon_H1b6 zenon_H122 zenon_H1e7 zenon_H1bd zenon_H11e zenon_H1cc zenon_H1cb zenon_H172 zenon_He9 zenon_H170 zenon_Hd7 zenon_H1ca zenon_H70 zenon_H142 zenon_H117 zenon_H152 zenon_H173 zenon_H165 zenon_H171 zenon_H113 zenon_H12e zenon_Hb3 zenon_H132 zenon_Hef zenon_H11f zenon_H153 zenon_H1c0 zenon_H177 zenon_H174 zenon_H176 zenon_H175 zenon_H1c5. % 4.78/4.94 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H2b | zenon_intro zenon_Hb4 ]. % 4.78/4.94 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H2c | zenon_intro zenon_H104 ]. % 4.78/4.94 apply (zenon_L280_); trivial. % 4.78/4.94 apply (zenon_L301_); trivial. % 4.78/4.94 apply (zenon_L293_); trivial. % 4.78/4.94 (* end of lemma zenon_L334_ *) % 4.78/4.94 assert (zenon_L335_ : ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> (~((op (e3) (e0)) = (op (e3) (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)) = (e0))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (((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))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (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))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> False). % 4.78/4.94 do 0 intro. intros zenon_H1b9 zenon_H175 zenon_H176 zenon_H174 zenon_H177 zenon_H1c0 zenon_H1bd zenon_H1e7 zenon_H122 zenon_H1b6 zenon_Haf zenon_H33 zenon_H19d zenon_Hc3 zenon_H86 zenon_H166 zenon_H1e8 zenon_H1e2 zenon_H1e1 zenon_H1de zenon_Hbe zenon_H153 zenon_H198 zenon_H194 zenon_Hf6 zenon_H195 zenon_H103 zenon_H1c4 zenon_H186 zenon_H100 zenon_Hfd zenon_H18f zenon_H1c5 zenon_H1e zenon_H114 zenon_H101 zenon_H54 zenon_H13c zenon_H28 zenon_Hef zenon_H137 zenon_H16b zenon_H89 zenon_H82 zenon_H9d zenon_H85 zenon_H94 zenon_H5b zenon_Hb9 zenon_H7b zenon_H135 zenon_H132 zenon_H36 zenon_H7c zenon_H1c7 zenon_H16c zenon_H4c zenon_H4b zenon_H179 zenon_Hd0 zenon_H1ab zenon_H118 zenon_H20 zenon_H21 zenon_H1d zenon_H11e zenon_H1cc zenon_H1cb zenon_H172 zenon_He9 zenon_H170 zenon_Hd7 zenon_H1ca zenon_H75 zenon_H70 zenon_H142 zenon_H117 zenon_H152 zenon_H6c zenon_H173 zenon_H165 zenon_H171 zenon_H13e zenon_H140 zenon_Hdf zenon_H95 zenon_H113 zenon_H12e zenon_Hb3 zenon_H11f zenon_H19a. % 4.78/4.94 apply (zenon_or_s _ _ zenon_H1b9); [ zenon_intro zenon_H29 | zenon_intro zenon_H145 ]. % 4.78/4.94 apply (zenon_or_s _ _ zenon_H19a); [ zenon_intro zenon_H2b | zenon_intro zenon_Hb4 ]. % 4.78/4.94 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H2c | zenon_intro zenon_H104 ]. % 4.78/4.94 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ]. % 4.78/4.94 exact (zenon_H1e zenon_H23). % 4.78/4.94 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ]. % 4.78/4.94 apply (zenon_or_s _ _ zenon_H114); [ zenon_intro zenon_H23 | zenon_intro zenon_H115 ]. % 4.78/4.94 exact (zenon_H1e zenon_H23). % 4.78/4.94 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H34 | zenon_intro zenon_H116 ]. % 4.78/4.94 apply (zenon_L305_); trivial. % 4.78/4.94 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H42 | zenon_intro zenon_Hbd ]. % 4.78/4.94 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H5a | zenon_intro zenon_H119 ]. % 4.78/4.94 exact (zenon_H5b zenon_H5a). % 4.78/4.94 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H9c | zenon_intro zenon_H11c ]. % 4.78/4.94 apply (zenon_L92_); trivial. % 4.78/4.94 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H87 ]. % 4.78/4.94 apply (zenon_L88_); trivial. % 4.78/4.94 apply (zenon_L276_); trivial. % 4.78/4.94 apply (zenon_L236_); trivial. % 4.78/4.94 apply (zenon_or_s _ _ zenon_H24); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 4.78/4.94 exact (zenon_H20 zenon_H27). % 4.78/4.94 exact (zenon_H21 zenon_H26). % 4.78/4.94 apply (zenon_L229_); trivial. % 4.78/4.94 apply (zenon_L259_); trivial. % 4.78/4.94 apply (zenon_L334_); trivial. % 4.78/4.94 (* end of lemma zenon_L335_ *) % 4.78/4.94 assert (zenon_L336_ : ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (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 (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (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 (e1) (e1)) = (e0))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((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))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> False). % 4.78/4.94 do 0 intro. intros zenon_H1ef zenon_H1f0 zenon_H1ed zenon_H1ee zenon_H1c5 zenon_H175 zenon_H176 zenon_H174 zenon_H177 zenon_H1c0 zenon_H153 zenon_H11f zenon_Hef zenon_H132 zenon_Hb3 zenon_H12e zenon_H113 zenon_H171 zenon_H165 zenon_H173 zenon_H152 zenon_H117 zenon_H142 zenon_H70 zenon_H1ca zenon_Hd7 zenon_H170 zenon_He9 zenon_H172 zenon_H1cb zenon_H1cc zenon_H11e zenon_H1bd zenon_H1e7 zenon_H122 zenon_H1b6 zenon_Haf zenon_H137 zenon_Hf6 zenon_H194 zenon_H33 zenon_H19d zenon_Hc3 zenon_Hfd zenon_H195 zenon_H7b zenon_Hdf zenon_H13e zenon_H103 zenon_H86 zenon_H166 zenon_H6c zenon_H100 zenon_H1e8 zenon_H1e zenon_H114 zenon_H1e2 zenon_H1e1 zenon_H101 zenon_H28 zenon_H13c zenon_H54 zenon_H82 zenon_H9d zenon_H94 zenon_H36 zenon_H16b zenon_H89 zenon_H5b zenon_Hb9 zenon_H1de zenon_H145 zenon_H140 zenon_H75 zenon_H198 zenon_Hbe zenon_H1c7 zenon_H16c zenon_H4b zenon_H179 zenon_Hd0 zenon_H1ab zenon_H118 zenon_H20 zenon_H21 zenon_H1d zenon_H19a. % 4.78/4.94 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H135 | zenon_intro zenon_H104 ]. % 4.78/4.94 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H4c | zenon_intro zenon_Hb4 ]. % 4.78/4.94 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H85 | zenon_intro zenon_H104 ]. % 4.78/4.94 apply (zenon_L334_); trivial. % 4.78/4.94 apply (zenon_L322_); trivial. % 4.78/4.94 apply (zenon_L294_); trivial. % 4.78/4.94 apply (zenon_L324_); trivial. % 4.78/4.94 (* end of lemma zenon_L336_ *) % 4.78/4.94 assert (zenon_L337_ : ((~((op (e1) (e3)) = (e1)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> (((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)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((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) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((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 (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> False). % 4.78/4.94 do 0 intro. intros zenon_H1f1 zenon_H1bf zenon_H1b9 zenon_H1e8 zenon_H166 zenon_H86 zenon_Hc3 zenon_H19d zenon_H33 zenon_Haf zenon_H1b6 zenon_H122 zenon_H1e7 zenon_H1bd zenon_H1c0 zenon_H177 zenon_H174 zenon_H176 zenon_H175 zenon_H1e2 zenon_H1e1 zenon_H16b zenon_H89 zenon_H1de zenon_Hbe zenon_H179 zenon_H1c5 zenon_H18f zenon_H82 zenon_H9d zenon_Hfd zenon_H54 zenon_H100 zenon_H4b zenon_H186 zenon_H1c4 zenon_H1e zenon_H118 zenon_H101 zenon_H13c zenon_H28 zenon_Hef zenon_H103 zenon_H195 zenon_H16c zenon_Hf6 zenon_H194 zenon_H198 zenon_H104 zenon_H137 zenon_H7c zenon_H36 zenon_H132 zenon_H7b zenon_Hb9 zenon_H5b zenon_H20 zenon_H21 zenon_H1d zenon_H11e zenon_H1cc zenon_H1cb zenon_H172 zenon_He9 zenon_H1ab zenon_H170 zenon_H1c7 zenon_Hd7 zenon_H1ca zenon_H94 zenon_Hd0 zenon_H75 zenon_H70 zenon_H142 zenon_H117 zenon_H152 zenon_H6c zenon_H173 zenon_H165 zenon_H171 zenon_H13e zenon_H140 zenon_Hdf zenon_H113 zenon_H12e zenon_Hb3 zenon_H114 zenon_H11f zenon_H153 zenon_H19a zenon_H1ed zenon_H1bb zenon_H46 zenon_H1e9 zenon_H1ec zenon_H1ba zenon_H1ee zenon_H1f0 zenon_H1ef. % 4.78/4.94 apply (zenon_or_s _ _ zenon_H1f0); [ zenon_intro zenon_H135 | zenon_intro zenon_H38 ]. % 4.78/4.94 apply (zenon_L325_); trivial. % 4.78/4.94 apply (zenon_L331_); trivial. % 4.78/4.94 (* end of lemma zenon_L337_ *) % 4.78/4.94 assert (zenon_L338_ : ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> (~((op (e3) (e0)) = (op (e3) (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)) = (e0))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (((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))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> False). % 4.78/4.94 do 0 intro. intros zenon_H1bf zenon_H1f1 zenon_H1b9 zenon_H175 zenon_H176 zenon_H174 zenon_H177 zenon_H1c0 zenon_H1bd zenon_H1e7 zenon_H122 zenon_H1b6 zenon_Haf zenon_H33 zenon_H19d zenon_Hc3 zenon_H86 zenon_H166 zenon_H1e8 zenon_H1e2 zenon_H1e1 zenon_H1de zenon_Hbe zenon_H153 zenon_H198 zenon_H194 zenon_Hf6 zenon_H195 zenon_H103 zenon_H1c4 zenon_H186 zenon_H100 zenon_Hfd zenon_H18f zenon_H1c5 zenon_H1e zenon_H114 zenon_H101 zenon_H54 zenon_H13c zenon_H28 zenon_Hef zenon_H137 zenon_H16b zenon_H89 zenon_H82 zenon_H9d zenon_H94 zenon_H5b zenon_Hb9 zenon_H7b zenon_H132 zenon_H36 zenon_H7c zenon_H1c7 zenon_H16c zenon_H4b zenon_H179 zenon_Hd0 zenon_H1ab zenon_H118 zenon_H20 zenon_H21 zenon_H1d zenon_H11e zenon_H1cc zenon_H1cb zenon_H172 zenon_He9 zenon_H170 zenon_Hd7 zenon_H1ca zenon_H75 zenon_H70 zenon_H142 zenon_H117 zenon_H152 zenon_H6c zenon_H173 zenon_H165 zenon_H171 zenon_H13e zenon_H140 zenon_Hdf zenon_H113 zenon_H12e zenon_Hb3 zenon_H11f zenon_H19a zenon_H1ee zenon_H1ec zenon_H1e9 zenon_H46 zenon_H1ed zenon_H1ba zenon_H1bb zenon_H1ef zenon_H1f0. % 4.78/4.94 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H135 | zenon_intro zenon_H104 ]. % 4.78/4.94 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H95 | zenon_intro zenon_H145 ]. % 4.78/4.94 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H4c | zenon_intro zenon_Hb4 ]. % 4.78/4.94 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H85 | zenon_intro zenon_H104 ]. % 4.78/4.94 apply (zenon_L335_); trivial. % 4.78/4.94 apply (zenon_L319_); trivial. % 4.78/4.94 apply (zenon_L287_); trivial. % 4.78/4.94 apply (zenon_L336_); trivial. % 4.78/4.94 apply (zenon_L337_); trivial. % 4.78/4.94 (* end of lemma zenon_L338_ *) % 4.78/4.94 assert (zenon_L339_ : ((~((op (e1) (e3)) = (e1)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((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 (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> False). % 4.78/4.94 do 0 intro. intros zenon_H1f1 zenon_H1bf zenon_H1b6 zenon_H1ba zenon_H1c4 zenon_H1e zenon_H118 zenon_H101 zenon_H28 zenon_Hef zenon_H36 zenon_H198 zenon_H186 zenon_H13c zenon_H16c zenon_H4d zenon_H4b zenon_H104 zenon_H100 zenon_H54 zenon_H194 zenon_Hf6 zenon_Hfd zenon_H103 zenon_H9d zenon_H82 zenon_H18f zenon_H137 zenon_Hb9 zenon_H5b zenon_H20 zenon_H1d zenon_H11e zenon_H1cc zenon_H1cb zenon_H172 zenon_He9 zenon_H1ab zenon_H170 zenon_H1c7 zenon_Hd7 zenon_H1ca zenon_H94 zenon_Hd0 zenon_H75 zenon_H70 zenon_H142 zenon_H117 zenon_H152 zenon_H6c zenon_H173 zenon_H165 zenon_H171 zenon_H21 zenon_H13e zenon_H140 zenon_Hdf zenon_H113 zenon_H12e zenon_Hb3 zenon_H132 zenon_H7b zenon_H114 zenon_H11f zenon_H153 zenon_H19a zenon_H1bb zenon_H122 zenon_H1e7 zenon_H1bd zenon_H1c0 zenon_H177 zenon_H174 zenon_H176 zenon_H175 zenon_H19d zenon_H38 zenon_H33 zenon_H86 zenon_H46 zenon_Hbe zenon_H1e9 zenon_H1ec. % 4.78/4.94 apply (zenon_or_s _ _ zenon_H1c0); [ zenon_intro zenon_H7c | zenon_intro zenon_H179 ]. % 4.78/4.94 apply (zenon_or_s _ _ zenon_H1bf); [ zenon_intro zenon_H195 | zenon_intro zenon_Hb4 ]. % 4.78/4.94 apply (zenon_L328_); trivial. % 4.78/4.94 apply (zenon_L291_); trivial. % 4.78/4.94 apply (zenon_L299_); trivial. % 4.78/4.94 (* end of lemma zenon_L339_ *) % 4.78/4.94 assert (zenon_L340_ : ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e2) (e0)) = (op (e2) (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 (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((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 (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (e0))) -> (((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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> False). % 4.78/4.95 do 0 intro. intros zenon_H1b6 zenon_H19a zenon_H122 zenon_H1e7 zenon_H1bd zenon_H11e zenon_H1cc zenon_H1cb zenon_H172 zenon_H1ab zenon_H170 zenon_H1c7 zenon_Hd7 zenon_H1ca zenon_H94 zenon_Hd0 zenon_H70 zenon_H142 zenon_H117 zenon_H152 zenon_H173 zenon_H165 zenon_H171 zenon_H13e zenon_Hdf zenon_H12e zenon_Hb3 zenon_H82 zenon_H132 zenon_H7b zenon_H114 zenon_H11f zenon_H153 zenon_H1c0 zenon_H177 zenon_H174 zenon_H176 zenon_H175 zenon_H1e zenon_H118 zenon_H198 zenon_H7c zenon_H101 zenon_H13c zenon_H2c zenon_H28 zenon_Hef zenon_H36 zenon_H100 zenon_H104 zenon_H54 zenon_H194 zenon_Hf6 zenon_H16c zenon_H195 zenon_Hfd zenon_H103 zenon_H9d zenon_Hc3 zenon_H19d zenon_H38 zenon_H33 zenon_H4d zenon_H18f zenon_H137 zenon_Hb9 zenon_H5b zenon_H20 zenon_He9 zenon_H86 zenon_H46 zenon_H4b zenon_Hbe zenon_H75 zenon_H113 zenon_H140 zenon_H6c zenon_H1e9 zenon_H1d zenon_H1ba. % 4.78/4.95 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H4c | zenon_intro zenon_Hb4 ]. % 4.78/4.95 apply (zenon_L315_); trivial. % 4.78/4.95 apply (zenon_L73_); trivial. % 4.78/4.95 (* end of lemma zenon_L340_ *) % 4.78/4.95 assert (zenon_L341_ : ((~((op (e0) (e3)) = (e0)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (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 (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e3) (e3)) = (e3)))) -> False). % 4.78/4.95 do 0 intro. intros zenon_H1be zenon_H1ec zenon_H1e9 zenon_Hbe zenon_H46 zenon_H86 zenon_H33 zenon_H38 zenon_H19d zenon_H175 zenon_H176 zenon_H174 zenon_H177 zenon_H1c0 zenon_H1bd zenon_H1e7 zenon_H122 zenon_H1bb zenon_H19a zenon_H153 zenon_H11f zenon_H114 zenon_H7b zenon_H132 zenon_Hb3 zenon_H12e zenon_H113 zenon_Hdf zenon_H140 zenon_H13e zenon_H171 zenon_H165 zenon_H173 zenon_H6c zenon_H152 zenon_H117 zenon_H142 zenon_H70 zenon_H75 zenon_Hd0 zenon_H94 zenon_H1ca zenon_Hd7 zenon_H1c7 zenon_H170 zenon_H1ab zenon_He9 zenon_H172 zenon_H1cb zenon_H1cc zenon_H11e zenon_H1d zenon_H20 zenon_H5b zenon_Hb9 zenon_H137 zenon_H18f zenon_H82 zenon_H9d zenon_H103 zenon_Hfd zenon_Hf6 zenon_H194 zenon_H54 zenon_H100 zenon_H104 zenon_H4b zenon_H4d zenon_H16c zenon_H13c zenon_H186 zenon_H198 zenon_H36 zenon_Hef zenon_H28 zenon_H101 zenon_H118 zenon_H1e zenon_H1c4 zenon_H1ba zenon_H1b6 zenon_H1bf zenon_H1f1. % 4.78/4.95 apply (zenon_or_s _ _ zenon_H1be); [ zenon_intro zenon_H21 | zenon_intro zenon_H2c ]. % 4.78/4.95 apply (zenon_L339_); trivial. % 4.78/4.95 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H7c | zenon_intro zenon_Hc3 ]. % 4.78/4.95 apply (zenon_L327_); trivial. % 4.78/4.95 apply (zenon_or_s _ _ zenon_H1c0); [ zenon_intro zenon_H7c | zenon_intro zenon_H179 ]. % 4.78/4.95 apply (zenon_or_s _ _ zenon_H1bf); [ zenon_intro zenon_H195 | zenon_intro zenon_Hb4 ]. % 4.78/4.95 apply (zenon_L340_); trivial. % 4.78/4.95 apply (zenon_L298_); trivial. % 4.78/4.95 apply (zenon_L299_); trivial. % 4.78/4.95 (* end of lemma zenon_L341_ *) % 4.78/4.95 assert (zenon_L342_ : ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (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 (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e2) (e2)) = (e3)))) -> False). % 4.78/4.95 do 0 intro. intros zenon_H1c3 zenon_H1ef zenon_H1f0 zenon_H1ee zenon_H1ec zenon_H1e9 zenon_H46 zenon_H1ed zenon_H19a zenon_H153 zenon_H11f zenon_H114 zenon_Hb3 zenon_H12e zenon_H113 zenon_Hdf zenon_H140 zenon_H13e zenon_H171 zenon_H165 zenon_H173 zenon_H6c zenon_H152 zenon_H117 zenon_H142 zenon_H70 zenon_H75 zenon_Hd0 zenon_H94 zenon_H1ca zenon_Hd7 zenon_H1c7 zenon_H170 zenon_H1ab zenon_He9 zenon_H172 zenon_H1cb zenon_H1cc zenon_H11e zenon_H1d zenon_H5b zenon_Hb9 zenon_H132 zenon_H137 zenon_H198 zenon_H194 zenon_Hf6 zenon_H16c zenon_H103 zenon_Hef zenon_H28 zenon_H13c zenon_H101 zenon_H118 zenon_H1e zenon_H1c4 zenon_H186 zenon_H4b zenon_H100 zenon_H54 zenon_Hfd zenon_H9d zenon_H82 zenon_H18f zenon_H1c5 zenon_H1ba zenon_Hbe zenon_H1de zenon_H89 zenon_H16b zenon_H1e1 zenon_H1e2 zenon_H175 zenon_H176 zenon_H174 zenon_H177 zenon_H1c0 zenon_H1bd zenon_H1e7 zenon_H122 zenon_H1b6 zenon_Haf zenon_H33 zenon_H19d zenon_H86 zenon_H166 zenon_H1e8 zenon_H1b9 zenon_H1bb zenon_H1bf zenon_H1f1 zenon_H36 zenon_H7b zenon_H1c1 zenon_H1be zenon_H1c2. % 4.78/4.95 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H20 | zenon_intro zenon_Hb4 ]. % 4.78/4.95 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_H21 | zenon_intro zenon_H104 ]. % 4.78/4.95 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H7c | zenon_intro zenon_Hc3 ]. % 4.78/4.95 apply (zenon_or_s _ _ zenon_H1bf); [ zenon_intro zenon_H195 | zenon_intro zenon_Hb4 ]. % 4.78/4.95 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H135 | zenon_intro zenon_H104 ]. % 4.78/4.95 apply (zenon_L227_); trivial. % 4.78/4.95 apply (zenon_L332_); trivial. % 4.78/4.95 apply (zenon_L291_); trivial. % 4.78/4.95 apply (zenon_or_s _ _ zenon_H1c0); [ zenon_intro zenon_H7c | zenon_intro zenon_H179 ]. % 4.78/4.95 apply (zenon_or_s _ _ zenon_H1bf); [ zenon_intro zenon_H195 | zenon_intro zenon_Hb4 ]. % 4.78/4.95 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H135 | zenon_intro zenon_H104 ]. % 4.78/4.95 apply (zenon_L227_); trivial. % 4.78/4.95 apply (zenon_L333_); trivial. % 4.78/4.95 apply (zenon_L296_); trivial. % 4.78/4.95 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H7c | zenon_intro zenon_H145 ]. % 4.78/4.95 apply (zenon_or_s _ _ zenon_H1bf); [ zenon_intro zenon_H195 | zenon_intro zenon_Hb4 ]. % 4.78/4.95 apply (zenon_L338_); trivial. % 4.78/4.95 apply (zenon_L292_); trivial. % 4.78/4.95 apply (zenon_or_s _ _ zenon_H1bf); [ zenon_intro zenon_H195 | zenon_intro zenon_Hb4 ]. % 4.78/4.95 apply (zenon_L336_); trivial. % 4.78/4.95 apply (zenon_L295_); trivial. % 4.78/4.95 apply (zenon_or_s _ _ zenon_H1c1); [ zenon_intro zenon_H21 | zenon_intro zenon_H38 ]. % 4.78/4.95 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H7c | zenon_intro zenon_Hc3 ]. % 4.78/4.95 apply (zenon_or_s _ _ zenon_H1bf); [ zenon_intro zenon_H195 | zenon_intro zenon_Hb4 ]. % 4.78/4.95 apply (zenon_L332_); trivial. % 4.78/4.95 apply (zenon_L291_); trivial. % 4.78/4.95 apply (zenon_or_s _ _ zenon_H1c0); [ zenon_intro zenon_H7c | zenon_intro zenon_H179 ]. % 4.78/4.95 apply (zenon_L333_); trivial. % 4.78/4.95 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H7c | zenon_intro zenon_H145 ]. % 4.78/4.95 apply (zenon_or_s _ _ zenon_H1bf); [ zenon_intro zenon_H195 | zenon_intro zenon_Hb4 ]. % 4.78/4.95 apply (zenon_L337_); trivial. % 4.78/4.95 apply (zenon_L292_); trivial. % 4.78/4.95 apply (zenon_or_s _ _ zenon_H1bf); [ zenon_intro zenon_H195 | zenon_intro zenon_Hb4 ]. % 4.78/4.95 apply (zenon_L324_); trivial. % 4.78/4.95 apply (zenon_L295_); trivial. % 4.78/4.95 apply (zenon_or_s _ _ zenon_H1c2); [ zenon_intro zenon_H21 | zenon_intro zenon_H4d ]. % 4.78/4.95 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H7c | zenon_intro zenon_Hc3 ]. % 4.78/4.95 apply (zenon_L331_); trivial. % 4.78/4.95 apply (zenon_or_s _ _ zenon_H1c0); [ zenon_intro zenon_H7c | zenon_intro zenon_H179 ]. % 4.78/4.95 apply (zenon_or_s _ _ zenon_H1bf); [ zenon_intro zenon_H195 | zenon_intro zenon_Hb4 ]. % 4.78/4.95 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H135 | zenon_intro zenon_H4d ]. % 4.78/4.95 apply (zenon_L330_); trivial. % 4.78/4.95 apply (zenon_L339_); trivial. % 4.78/4.95 apply (zenon_L73_); trivial. % 4.78/4.95 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H7c | zenon_intro zenon_H145 ]. % 4.78/4.95 apply (zenon_or_s _ _ zenon_H1bf); [ zenon_intro zenon_H195 | zenon_intro zenon_Hb4 ]. % 4.78/4.95 apply (zenon_L329_); trivial. % 4.78/4.95 apply (zenon_L292_); trivial. % 4.78/4.95 apply (zenon_or_s _ _ zenon_H1bf); [ zenon_intro zenon_H195 | zenon_intro zenon_Hb4 ]. % 4.78/4.95 apply (zenon_L323_); trivial. % 4.78/4.95 apply (zenon_L295_); trivial. % 4.78/4.95 apply (zenon_L341_); trivial. % 4.78/4.95 apply (zenon_L298_); trivial. % 4.78/4.95 (* end of lemma zenon_L342_ *) % 4.78/4.95 assert (zenon_L343_ : ((~((op (e0) (e1)) = (e0)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> (((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 (e1) (e1)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (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))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (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 (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e1) (e1)) = (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> False). % 4.78/4.95 do 0 intro. intros zenon_H1f2 zenon_H1ef zenon_H1f0 zenon_H1ee zenon_H1ec zenon_H1e9 zenon_H46 zenon_H1ed zenon_H6c zenon_H1ca zenon_Hd7 zenon_H1c7 zenon_H1cb zenon_H1cc zenon_H11e zenon_H1c4 zenon_H1c5 zenon_H1de zenon_H89 zenon_H1e1 zenon_H1e2 zenon_H1bd zenon_H1e7 zenon_H33 zenon_H19d zenon_H1e8 zenon_H1b9 zenon_H1f1 zenon_H1f3 zenon_H1c2 zenon_H1c0 zenon_H1b6 zenon_H19b zenon_H18f zenon_Hf6 zenon_H194 zenon_H4b zenon_H186 zenon_H198 zenon_Hef zenon_H101 zenon_H28 zenon_H175 zenon_H176 zenon_H174 zenon_H173 zenon_H172 zenon_H16f zenon_H16b zenon_He9 zenon_H166 zenon_H86 zenon_H165 zenon_Hbe zenon_H170 zenon_H152 zenon_H114 zenon_H7b zenon_H132 zenon_H36 zenon_H100 zenon_Hd0 zenon_H94 zenon_H137 zenon_Hac zenon_H82 zenon_Ha0 zenon_Ha4 zenon_Ha9 zenon_H9d zenon_Haf zenon_Hb3 zenon_Hb9 zenon_H12e zenon_H118 zenon_Hdf zenon_H13e zenon_H117 zenon_H142 zenon_H70 zenon_H75 zenon_H113 zenon_H54 zenon_Hfd zenon_H13c zenon_H103 zenon_H153 zenon_H154 zenon_H171 zenon_H177 zenon_H11f zenon_H5b zenon_H122 zenon_H19a zenon_H1ba zenon_H1ab zenon_H41 zenon_H1bb zenon_H1bf zenon_H1be zenon_H1c1 zenon_H1e zenon_H1d zenon_H1c3. % 4.78/4.95 apply (zenon_or_s _ _ zenon_H1f2); [ zenon_intro zenon_H1f | zenon_intro zenon_H16c ]. % 4.78/4.95 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H20 | zenon_intro zenon_Hb4 ]. % 4.78/4.95 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_H21 | zenon_intro zenon_H104 ]. % 4.78/4.95 apply (zenon_L1_); trivial. % 4.78/4.95 apply (zenon_L219_); trivial. % 4.78/4.95 apply (zenon_L138_); trivial. % 4.78/4.95 apply (zenon_or_s _ _ zenon_H1f3); [ zenon_intro zenon_H1f | zenon_intro zenon_H140 ]. % 4.78/4.95 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H20 | zenon_intro zenon_Hb4 ]. % 4.78/4.95 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_H21 | zenon_intro zenon_H104 ]. % 4.78/4.95 apply (zenon_L1_); trivial. % 4.78/4.95 apply (zenon_or_s _ _ zenon_H1c2); [ zenon_intro zenon_H21 | zenon_intro zenon_H4d ]. % 4.78/4.95 apply (zenon_L1_); trivial. % 4.78/4.95 apply (zenon_or_s _ _ zenon_H1be); [ zenon_intro zenon_H21 | zenon_intro zenon_H2c ]. % 4.78/4.95 apply (zenon_L1_); trivial. % 4.78/4.95 apply (zenon_or_s _ _ zenon_H1c0); [ zenon_intro zenon_H7c | zenon_intro zenon_H179 ]. % 4.78/4.95 apply (zenon_L225_); trivial. % 4.78/4.95 apply (zenon_L226_); trivial. % 4.78/4.95 apply (zenon_L224_); trivial. % 4.78/4.95 apply (zenon_L342_); trivial. % 4.78/4.95 (* end of lemma zenon_L343_ *) % 4.78/4.95 assert (zenon_L344_ : ((~((op (e0) (e1)) = (e0)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((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))))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (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)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((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 (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (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)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((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 (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> False). % 4.78/4.95 do 0 intro. intros zenon_H1f4 zenon_H1f3 zenon_H1f1 zenon_H1b9 zenon_H1e8 zenon_H19d zenon_H33 zenon_H1e7 zenon_H1bd zenon_H1e2 zenon_H1e1 zenon_H89 zenon_H1de zenon_H1c5 zenon_H1c4 zenon_H11e zenon_H1cc zenon_H1cb zenon_H1c7 zenon_Hd7 zenon_H1ca zenon_H6c zenon_H1ed zenon_H46 zenon_H1e9 zenon_H1ec zenon_H1ee zenon_H1f0 zenon_H1ef zenon_H1f2 zenon_H1c1 zenon_H1be zenon_H1bf zenon_H1bb zenon_H41 zenon_H1ab zenon_H1ba zenon_H19a zenon_H122 zenon_H5b zenon_H11f zenon_H177 zenon_H171 zenon_H154 zenon_H153 zenon_H103 zenon_H13c zenon_Hfd zenon_H54 zenon_H113 zenon_H75 zenon_H70 zenon_H142 zenon_H117 zenon_H13e zenon_Hdf zenon_H118 zenon_H12e zenon_Hb9 zenon_Hb3 zenon_Haf zenon_H9d zenon_Ha9 zenon_Ha4 zenon_Ha0 zenon_H82 zenon_Hac zenon_H137 zenon_H94 zenon_Hd0 zenon_H100 zenon_H132 zenon_H7b zenon_H114 zenon_H152 zenon_H170 zenon_Hbe zenon_H165 zenon_H86 zenon_H166 zenon_He9 zenon_H16b zenon_H16f zenon_H172 zenon_H173 zenon_H174 zenon_H176 zenon_H175 zenon_H28 zenon_H101 zenon_Hef zenon_H198 zenon_H186 zenon_H4b zenon_H194 zenon_Hf6 zenon_H18f zenon_H19b zenon_H1b6 zenon_H1c0 zenon_H1c2 zenon_H1b7 zenon_H1e zenon_H1d zenon_H1c3. % 4.78/4.95 apply (zenon_or_s _ _ zenon_H1f4); [ zenon_intro zenon_H1f | zenon_intro zenon_H36 ]. % 4.78/4.95 apply (zenon_L223_); trivial. % 4.78/4.95 apply (zenon_L343_); trivial. % 4.78/4.95 (* end of lemma zenon_L344_ *) % 4.78/4.95 assert (zenon_L345_ : ((~((op (e3) (e1)) = (e3)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e1) (e1)) = (e1)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 4.78/4.95 do 0 intro. intros zenon_H19c zenon_H1c3 zenon_H1b7 zenon_H1c2 zenon_H1c0 zenon_H1b6 zenon_H19b zenon_H18f zenon_H194 zenon_H186 zenon_H198 zenon_H28 zenon_H175 zenon_H176 zenon_H174 zenon_H173 zenon_H172 zenon_H16f zenon_H16b zenon_H166 zenon_H165 zenon_H170 zenon_H152 zenon_H132 zenon_H137 zenon_H12e zenon_H13e zenon_H142 zenon_H13c zenon_H153 zenon_H154 zenon_H171 zenon_H177 zenon_H11f zenon_H122 zenon_H19a zenon_H1ba zenon_H1ab zenon_H1bb zenon_H1bf zenon_H1be zenon_H1c1 zenon_H1f2 zenon_H1ef zenon_H1f0 zenon_H1ee zenon_H1ec zenon_H1e9 zenon_H1ed zenon_H1ca zenon_H1c7 zenon_H1cb zenon_H1cc zenon_H11e zenon_H1c4 zenon_H1c5 zenon_H1de zenon_H1e1 zenon_H1e2 zenon_H1bd zenon_H1e7 zenon_H19d zenon_H1e8 zenon_H1b9 zenon_H1f1 zenon_H1f3 zenon_H1f4 zenon_H1e zenon_H1f zenon_H114 zenon_H113 zenon_H110 zenon_H104 zenon_He9 zenon_He6 zenon_Hdc zenon_Hda zenon_Hd7 zenon_Hdf zenon_Hd0 zenon_Hbe zenon_H102 zenon_Hf6 zenon_Hef zenon_Hf3 zenon_Hf9 zenon_H101 zenon_H103 zenon_Hfd zenon_H100 zenon_H7c zenon_H4b zenon_H4d zenon_H4c zenon_H46 zenon_H41 zenon_H94 zenon_H54 zenon_H117 zenon_H86 zenon_H89 zenon_H8f zenon_H82 zenon_H7b zenon_H6c zenon_H70 zenon_H76 zenon_H2c zenon_H75 zenon_He2 zenon_H96 zenon_H95 zenon_Hb4 zenon_Hb3 zenon_Haf zenon_H9d zenon_Ha9 zenon_Ha4 zenon_Ha0 zenon_Hac zenon_Hb9 zenon_H118 zenon_H35 zenon_H36 zenon_H37 zenon_H38 zenon_H33 zenon_H1d. % 4.78/4.95 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H2a | zenon_intro zenon_H5b ]. % 4.78/4.95 apply (zenon_L70_); trivial. % 4.78/4.95 apply (zenon_L344_); trivial. % 4.78/4.95 (* end of lemma zenon_L345_ *) % 4.78/4.95 assert (zenon_L346_ : ((~((op (e3) (e1)) = (e3)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e1) (e1)) = (e1)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e0) (e0)) = (e1)))) -> False). % 4.78/4.95 do 0 intro. intros zenon_H19c zenon_H1c3 zenon_H1b7 zenon_H1c2 zenon_H1c0 zenon_H1b6 zenon_H19b zenon_H18f zenon_H194 zenon_H186 zenon_H198 zenon_H28 zenon_H175 zenon_H176 zenon_H174 zenon_H173 zenon_H172 zenon_H16f zenon_H16b zenon_H166 zenon_H165 zenon_H170 zenon_H152 zenon_H132 zenon_H137 zenon_H12e zenon_H13e zenon_H142 zenon_H13c zenon_H153 zenon_H154 zenon_H171 zenon_H177 zenon_H11f zenon_H122 zenon_H19a zenon_H1ba zenon_H1ab zenon_H1bb zenon_H1bf zenon_H1be zenon_H1c1 zenon_H1f2 zenon_H1ef zenon_H1f0 zenon_H1ee zenon_H1ec zenon_H1e9 zenon_H1ed zenon_H1ca zenon_H1c7 zenon_H1cb zenon_H1cc zenon_H11e zenon_H1c4 zenon_H1c5 zenon_H1de zenon_H1e1 zenon_H1e2 zenon_H1bd zenon_H1e7 zenon_H19d zenon_H1e8 zenon_H1b9 zenon_H1f1 zenon_H1f3 zenon_H1f4 zenon_H1e zenon_H1f zenon_H114 zenon_H113 zenon_H110 zenon_H104 zenon_He9 zenon_He6 zenon_Hdc zenon_Hda zenon_Hd7 zenon_Hdf zenon_Hd0 zenon_Hbe zenon_H102 zenon_Hf6 zenon_Hef zenon_Hf3 zenon_Hf9 zenon_H101 zenon_H103 zenon_Hfd zenon_H100 zenon_H7c zenon_H4b zenon_H4d zenon_H4c zenon_H46 zenon_H41 zenon_H94 zenon_H54 zenon_H117 zenon_H86 zenon_H89 zenon_H8f zenon_H82 zenon_H7b zenon_H6c zenon_H70 zenon_H76 zenon_H2c zenon_H75 zenon_He2 zenon_Hb4 zenon_Hb3 zenon_Haf zenon_H9d zenon_Ha9 zenon_Ha4 zenon_Ha0 zenon_Hac zenon_Hb9 zenon_H118 zenon_H35 zenon_H36 zenon_H37 zenon_H38 zenon_H33 zenon_H1d zenon_H1f5. % 4.78/4.95 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H95 | zenon_intro zenon_Hc3 ]. % 4.78/4.95 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_H96 | zenon_intro zenon_H5b ]. % 4.78/4.95 apply (zenon_L345_); trivial. % 4.78/4.95 apply (zenon_L137_); trivial. % 4.78/4.95 apply (zenon_L189_); trivial. % 4.78/4.95 (* end of lemma zenon_L346_ *) % 4.78/4.95 assert (zenon_L347_ : ((~((op (e1) (e1)) = (e1)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e0) (e0)) = (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((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)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (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 (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (~((e1) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e0) (e0)) = (e1)))) -> False). % 4.78/4.96 do 0 intro. intros zenon_H1b8 zenon_H1f5 zenon_H1d zenon_H33 zenon_H38 zenon_H37 zenon_H35 zenon_H118 zenon_Hb9 zenon_Hac zenon_Ha0 zenon_Ha4 zenon_Ha9 zenon_H9d zenon_Haf zenon_Hb3 zenon_Hb4 zenon_He2 zenon_H75 zenon_H2c zenon_H76 zenon_H70 zenon_H6c zenon_H7b zenon_H82 zenon_H8f zenon_H89 zenon_H86 zenon_H117 zenon_H54 zenon_H94 zenon_H41 zenon_H46 zenon_H4c zenon_H4d zenon_H4b zenon_H7c zenon_H100 zenon_Hfd zenon_H103 zenon_H101 zenon_Hf9 zenon_Hf3 zenon_Hef zenon_Hf6 zenon_H102 zenon_Hbe zenon_Hd0 zenon_Hdf zenon_Hd7 zenon_Hda zenon_Hdc zenon_He6 zenon_He9 zenon_H104 zenon_H110 zenon_H113 zenon_H114 zenon_H1f zenon_H1e zenon_H1f4 zenon_H1f3 zenon_H1f1 zenon_H1b9 zenon_H1e8 zenon_H19d zenon_H1e7 zenon_H1bd zenon_H1e2 zenon_H1e1 zenon_H1de zenon_H1c5 zenon_H1c4 zenon_H11e zenon_H1cc zenon_H1cb zenon_H1c7 zenon_H1ca zenon_H1ed zenon_H1e9 zenon_H1ec zenon_H1ee zenon_H1f0 zenon_H1ef zenon_H1f2 zenon_H1c1 zenon_H1be zenon_H1bf zenon_H1bb zenon_H1ab zenon_H1ba zenon_H19a zenon_H122 zenon_H11f zenon_H177 zenon_H171 zenon_H154 zenon_H153 zenon_H13c zenon_H142 zenon_H13e zenon_H12e zenon_H137 zenon_H132 zenon_H152 zenon_H170 zenon_H165 zenon_H166 zenon_H16b zenon_H16f zenon_H172 zenon_H173 zenon_H174 zenon_H176 zenon_H175 zenon_H28 zenon_H198 zenon_H186 zenon_H194 zenon_H18f zenon_H19b zenon_H1b6 zenon_H1c0 zenon_H1c2 zenon_H1b7 zenon_H1c3 zenon_H19c. % 4.78/4.96 apply (zenon_or_s _ _ zenon_H1b8); [ zenon_intro zenon_H36 | zenon_intro zenon_H5b ]. % 4.78/4.96 apply (zenon_L346_); trivial. % 4.78/4.96 apply (zenon_L344_); trivial. % 4.78/4.96 (* end of lemma zenon_L347_ *) % 4.78/4.96 assert (zenon_L348_ : ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e0) (e0)) = (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (~((e1) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (e0))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (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 (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> False). % 4.78/4.96 do 0 intro. intros zenon_H1c3 zenon_H1c2 zenon_H1c0 zenon_H1bf zenon_H1be zenon_H1c1 zenon_H1f2 zenon_H1ef zenon_H1f0 zenon_H1ee zenon_H1ec zenon_H1e9 zenon_H1ed zenon_H1ca zenon_H1c7 zenon_H1cb zenon_H1cc zenon_H11e zenon_H1c4 zenon_H1c5 zenon_H1de zenon_H1e1 zenon_H1e2 zenon_H1bd zenon_H1e7 zenon_H19d zenon_H1e8 zenon_H1b9 zenon_H1f1 zenon_H1f3 zenon_H1f4 zenon_H1f5 zenon_H1ab zenon_H1ba zenon_H1b6 zenon_H19c zenon_H19a zenon_H122 zenon_H11f zenon_H177 zenon_H171 zenon_H154 zenon_H153 zenon_H13c zenon_H142 zenon_H13e zenon_H12e zenon_H137 zenon_H132 zenon_H152 zenon_H170 zenon_H165 zenon_H166 zenon_H16b zenon_H16f zenon_H172 zenon_H173 zenon_H174 zenon_H176 zenon_H175 zenon_H198 zenon_H186 zenon_H194 zenon_H18f zenon_H20 zenon_H19b zenon_H28 zenon_H2c zenon_H1d zenon_H33 zenon_H38 zenon_H37 zenon_H36 zenon_H35 zenon_H118 zenon_Hb9 zenon_Hac zenon_Ha0 zenon_Ha4 zenon_Ha9 zenon_H9d zenon_Haf zenon_Hb3 zenon_Hb4 zenon_He2 zenon_H75 zenon_H70 zenon_H6c zenon_H7b zenon_H82 zenon_H8f zenon_H89 zenon_H86 zenon_H117 zenon_H54 zenon_H94 zenon_H41 zenon_H46 zenon_H4c zenon_H4d zenon_H4b zenon_H7c zenon_H100 zenon_Hfd zenon_H103 zenon_H101 zenon_Hf9 zenon_Hf3 zenon_Hef zenon_Hf6 zenon_H102 zenon_Hbe zenon_Hd0 zenon_Hdf zenon_Hd7 zenon_Hda zenon_Hdc zenon_He6 zenon_He9 zenon_H104 zenon_H110 zenon_H113 zenon_H114 zenon_H1f zenon_H1e zenon_H11d zenon_H1b8 zenon_H1b7 zenon_H1bb. % 4.78/4.96 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H195 | zenon_intro zenon_H76 ]. % 4.78/4.96 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H95 | zenon_intro zenon_Hc3 ]. % 4.78/4.96 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_H96 | zenon_intro zenon_H5b ]. % 4.78/4.96 apply (zenon_L211_); trivial. % 4.78/4.96 apply (zenon_L215_); trivial. % 4.78/4.96 apply (zenon_L189_); trivial. % 4.78/4.96 apply (zenon_L347_); trivial. % 4.78/4.96 (* end of lemma zenon_L348_ *) % 4.78/4.96 assert (zenon_L349_ : ((~((op (e0) (e1)) = (e0)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e0) (e0)) = (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (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 (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> False). % 4.78/4.96 do 0 intro. intros zenon_H1f4 zenon_H1f3 zenon_H1f1 zenon_H1b9 zenon_H1e8 zenon_H19d zenon_H1e7 zenon_H1bd zenon_H1e2 zenon_H1e1 zenon_H1de zenon_H1c5 zenon_H1c4 zenon_H11e zenon_H1cc zenon_H1cb zenon_H1c7 zenon_H1ca zenon_H1ed zenon_H1e9 zenon_H1ec zenon_H1ee zenon_H1f0 zenon_H1ef zenon_H1f2 zenon_H1c1 zenon_H1be zenon_H1bf zenon_H1c0 zenon_H1c2 zenon_H1c3 zenon_H1f5 zenon_H1ab zenon_H1ba zenon_H1b6 zenon_H1bb zenon_H1b7 zenon_H1b8 zenon_H11d zenon_H1e zenon_H1f zenon_H114 zenon_H113 zenon_H110 zenon_H104 zenon_He9 zenon_He6 zenon_Hdc zenon_Hda zenon_Hd7 zenon_Hdf zenon_Hd0 zenon_Hbe zenon_H102 zenon_Hf6 zenon_Hef zenon_Hf3 zenon_Hf9 zenon_H101 zenon_H103 zenon_Hfd zenon_H100 zenon_H7c zenon_H4b zenon_H4d zenon_H46 zenon_H41 zenon_H94 zenon_H54 zenon_H117 zenon_H86 zenon_H89 zenon_H8f zenon_H82 zenon_H7b zenon_H6c zenon_H70 zenon_H75 zenon_He2 zenon_Hb4 zenon_Hb3 zenon_Haf zenon_H9d zenon_Ha9 zenon_Ha4 zenon_Ha0 zenon_Hac zenon_Hb9 zenon_H118 zenon_H35 zenon_H36 zenon_H37 zenon_H38 zenon_H33 zenon_H1d zenon_H2c zenon_H28 zenon_H19b zenon_H20 zenon_H18f zenon_H194 zenon_H186 zenon_H198 zenon_H175 zenon_H176 zenon_H174 zenon_H173 zenon_H172 zenon_H16f zenon_H16b zenon_H166 zenon_H165 zenon_H170 zenon_H152 zenon_H132 zenon_H137 zenon_H12e zenon_H13e zenon_H142 zenon_H13c zenon_H153 zenon_H154 zenon_H171 zenon_H177 zenon_H11f zenon_H122 zenon_H19a zenon_H19c zenon_H1bc. % 4.78/4.96 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H195 | zenon_intro zenon_H4c ]. % 4.78/4.96 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H95 | zenon_intro zenon_Hc3 ]. % 4.78/4.96 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_H96 | zenon_intro zenon_H5b ]. % 4.78/4.96 apply (zenon_L212_); trivial. % 4.78/4.96 apply (zenon_L215_); trivial. % 4.78/4.96 apply (zenon_L189_); trivial. % 4.78/4.96 apply (zenon_L348_); trivial. % 4.78/4.96 (* end of lemma zenon_L349_ *) % 4.78/4.96 assert (zenon_L350_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e0))) -> False). % 4.78/4.96 do 0 intro. intros zenon_H1d zenon_H1e zenon_H1f zenon_H89 zenon_H4c zenon_H96 zenon_H95 zenon_H94 zenon_H82 zenon_Hd0 zenon_H85 zenon_Hb4 zenon_H100 zenon_H21. % 4.78/4.96 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ]. % 4.78/4.96 exact (zenon_H1e zenon_H23). % 4.78/4.96 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ]. % 4.78/4.96 exact (zenon_H1f zenon_H25). % 4.78/4.96 apply (zenon_or_s _ _ zenon_H24); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 4.78/4.96 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hb6 | zenon_intro zenon_H105 ]. % 4.78/4.96 exact (zenon_Hb4 zenon_Hb6). % 4.78/4.96 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H5e | zenon_intro zenon_H106 ]. % 4.78/4.96 apply (zenon_L89_); trivial. % 4.78/4.96 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_H92 | zenon_intro zenon_H8a ]. % 4.78/4.96 apply (zenon_L23_); trivial. % 4.78/4.96 apply (zenon_L24_); trivial. % 4.78/4.96 exact (zenon_H21 zenon_H26). % 4.78/4.96 (* end of lemma zenon_L350_ *) % 4.78/4.96 assert (zenon_L351_ : ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (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 (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 4.78/4.96 do 0 intro. intros zenon_H1c4 zenon_H1e zenon_H1f zenon_H114 zenon_H113 zenon_H2a zenon_H110 zenon_H104 zenon_He9 zenon_He6 zenon_Hdc zenon_Hda zenon_Hd7 zenon_Hdf zenon_Hd0 zenon_Hbe zenon_H102 zenon_Hf6 zenon_Hef zenon_Hf3 zenon_Hf9 zenon_H101 zenon_H103 zenon_Hfd zenon_H100 zenon_H7c zenon_H4b zenon_H4d zenon_H4c zenon_H46 zenon_H41 zenon_H94 zenon_H54 zenon_H117 zenon_H86 zenon_H89 zenon_H8f zenon_H82 zenon_H7b zenon_H6c zenon_H70 zenon_H76 zenon_H75 zenon_He2 zenon_H96 zenon_H95 zenon_Hb4 zenon_Hb3 zenon_Haf zenon_H9d zenon_Ha9 zenon_Ha4 zenon_Ha0 zenon_Hac zenon_Hb9 zenon_H118 zenon_H35 zenon_H36 zenon_H37 zenon_H38 zenon_H33 zenon_H1d. % 4.78/4.96 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H2c | zenon_intro zenon_H2c ]. % 4.78/4.96 apply (zenon_L70_); trivial. % 4.78/4.96 apply (zenon_L70_); trivial. % 4.78/4.96 (* end of lemma zenon_L351_ *) % 4.78/4.96 assert (zenon_L352_ : ((~((op (e0) (e1)) = (e0)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (~((e1) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (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 (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (e1))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e0) (e0)) = (e1)))) -> False). % 4.78/4.96 do 0 intro. intros zenon_H1f4 zenon_H1f3 zenon_H1f1 zenon_H1b9 zenon_H1e8 zenon_H19d zenon_H1e7 zenon_H1bd zenon_H1e2 zenon_H1e1 zenon_H1de zenon_H1c5 zenon_H11e zenon_H1cc zenon_H1cb zenon_H1c7 zenon_H1ca zenon_H1ed zenon_H1e9 zenon_H1ec zenon_H1ee zenon_H1f0 zenon_H1ef zenon_H1f2 zenon_H1c1 zenon_H1be zenon_H1bf zenon_H1bb zenon_H1ab zenon_H1ba zenon_H19a zenon_H122 zenon_H177 zenon_H171 zenon_H154 zenon_H153 zenon_H13c zenon_H142 zenon_H13e zenon_H152 zenon_H170 zenon_H165 zenon_H166 zenon_H16b zenon_H16f zenon_H172 zenon_H173 zenon_H174 zenon_H176 zenon_H175 zenon_H28 zenon_H198 zenon_H186 zenon_H194 zenon_H18f zenon_H19b zenon_H1b6 zenon_H1c0 zenon_H1c2 zenon_H1b7 zenon_H1c3 zenon_H1c4 zenon_H1e zenon_H1f zenon_H114 zenon_H113 zenon_H110 zenon_H104 zenon_He9 zenon_He6 zenon_Hdc zenon_Hda zenon_Hd7 zenon_Hdf zenon_Hd0 zenon_Hbe zenon_H102 zenon_Hf6 zenon_Hef zenon_Hf3 zenon_Hf9 zenon_H101 zenon_H103 zenon_Hfd zenon_H100 zenon_H7c zenon_H4b zenon_H4d zenon_H4c zenon_H46 zenon_H41 zenon_H94 zenon_H54 zenon_H117 zenon_H86 zenon_H89 zenon_H8f zenon_H82 zenon_H7b zenon_H6c zenon_H70 zenon_H76 zenon_H75 zenon_He2 zenon_H96 zenon_H95 zenon_Hb4 zenon_Hb3 zenon_Haf zenon_H9d zenon_Ha9 zenon_Ha4 zenon_Ha0 zenon_Hac zenon_Hb9 zenon_H118 zenon_H35 zenon_H36 zenon_H37 zenon_H38 zenon_H33 zenon_H1d zenon_H21 zenon_H11f zenon_H12e zenon_H137 zenon_H132 zenon_H135 zenon_H19c. % 4.78/4.96 apply (zenon_or_s _ _ zenon_H1ec); [ zenon_intro zenon_H85 | zenon_intro zenon_H2c ]. % 4.78/4.96 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H2a | zenon_intro zenon_H5b ]. % 4.78/4.96 apply (zenon_L351_); trivial. % 4.78/4.96 apply (zenon_L91_); trivial. % 4.78/4.96 apply (zenon_L345_); trivial. % 4.78/4.96 (* end of lemma zenon_L352_ *) % 4.78/4.96 assert (zenon_L353_ : ((~((op (e3) (e1)) = (e3)))\/(~((op (e0) (e0)) = (e1)))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((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 (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((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)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (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 (e1) (e0)) = (e1))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e1) (e1)) = (e1)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 4.78/4.96 do 0 intro. intros zenon_H19c zenon_H135 zenon_H132 zenon_H137 zenon_H12e zenon_H11f zenon_H33 zenon_H38 zenon_H37 zenon_H36 zenon_H35 zenon_H118 zenon_Hb9 zenon_Hac zenon_Ha0 zenon_Ha4 zenon_Ha9 zenon_H9d zenon_Haf zenon_Hb3 zenon_He2 zenon_H75 zenon_H76 zenon_H70 zenon_H6c zenon_H7b zenon_H8f zenon_H86 zenon_H117 zenon_H54 zenon_H41 zenon_H46 zenon_H4b zenon_H7c zenon_Hfd zenon_H103 zenon_H101 zenon_Hf9 zenon_Hf3 zenon_Hef zenon_Hf6 zenon_H102 zenon_Hbe zenon_Hdf zenon_Hd7 zenon_Hda zenon_Hdc zenon_He6 zenon_He9 zenon_H104 zenon_H110 zenon_H113 zenon_H114 zenon_H1c4 zenon_H1c3 zenon_H1b7 zenon_H1c2 zenon_H1c0 zenon_H1b6 zenon_H19b zenon_H18f zenon_H194 zenon_H186 zenon_H198 zenon_H28 zenon_H175 zenon_H176 zenon_H174 zenon_H173 zenon_H172 zenon_H16f zenon_H16b zenon_H166 zenon_H165 zenon_H170 zenon_H152 zenon_H13e zenon_H142 zenon_H13c zenon_H153 zenon_H154 zenon_H171 zenon_H177 zenon_H122 zenon_H19a zenon_H1ba zenon_H1ab zenon_H1bb zenon_H1bf zenon_H1be zenon_H1c1 zenon_H1f2 zenon_H1ef zenon_H1f0 zenon_H1ee zenon_H1ec zenon_H1e9 zenon_H1ed zenon_H1ca zenon_H1c7 zenon_H1cb zenon_H1cc zenon_H11e zenon_H1c5 zenon_H1de zenon_H1e1 zenon_H1e2 zenon_H1bd zenon_H1e7 zenon_H19d zenon_H1e8 zenon_H1b9 zenon_H1f1 zenon_H1f3 zenon_H1f4 zenon_H1e zenon_H1f zenon_H100 zenon_H96 zenon_H89 zenon_H82 zenon_H95 zenon_Hd0 zenon_H4c zenon_H94 zenon_Hb4 zenon_H21 zenon_H1d. % 4.78/4.96 apply (zenon_or_s _ _ zenon_H1ed); [ zenon_intro zenon_H85 | zenon_intro zenon_H4d ]. % 4.78/4.96 apply (zenon_L350_); trivial. % 4.78/4.96 apply (zenon_L352_); trivial. % 4.78/4.96 (* end of lemma zenon_L353_ *) % 4.78/4.96 assert (zenon_L354_ : ((~((op (e0) (e1)) = (e0)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (~((e1) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (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) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (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 (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (e1))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e0) (e0)) = (e1)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 4.78/4.96 do 0 intro. intros zenon_H1f4 zenon_H1f3 zenon_H1f1 zenon_H1b9 zenon_H1e8 zenon_H19d zenon_H1e7 zenon_H1bd zenon_H1e2 zenon_H1e1 zenon_H1de zenon_H1c5 zenon_H11e zenon_H1cc zenon_H1cb zenon_H1c7 zenon_H1ca zenon_H1ed zenon_H1e9 zenon_H1ec zenon_H1ee zenon_H1f0 zenon_H1ef zenon_H1f2 zenon_H1c1 zenon_H1be zenon_H1bf zenon_H1bb zenon_H1ab zenon_H1ba zenon_H19a zenon_H122 zenon_H177 zenon_H171 zenon_H154 zenon_H153 zenon_H13c zenon_H142 zenon_H13e zenon_H152 zenon_H170 zenon_H165 zenon_H166 zenon_H16b zenon_H16f zenon_H172 zenon_H173 zenon_H174 zenon_H176 zenon_H175 zenon_H28 zenon_H198 zenon_H186 zenon_H194 zenon_H18f zenon_H19b zenon_H1b6 zenon_H1c0 zenon_H1c2 zenon_H1b7 zenon_H1c3 zenon_H1c4 zenon_H114 zenon_H113 zenon_H110 zenon_H104 zenon_He9 zenon_He6 zenon_Hdc zenon_Hda zenon_Hd7 zenon_Hdf zenon_Hbe zenon_H102 zenon_Hf6 zenon_Hef zenon_Hf3 zenon_Hf9 zenon_H101 zenon_H103 zenon_Hfd zenon_H7c zenon_H4b zenon_H46 zenon_H41 zenon_H54 zenon_H117 zenon_H86 zenon_H8f zenon_H7b zenon_H6c zenon_H70 zenon_H76 zenon_H75 zenon_He2 zenon_Hb3 zenon_Haf zenon_H9d zenon_Ha9 zenon_Ha4 zenon_Ha0 zenon_Hac zenon_Hb9 zenon_H118 zenon_H35 zenon_H36 zenon_H37 zenon_H33 zenon_H11f zenon_H12e zenon_H137 zenon_H132 zenon_H135 zenon_H19c zenon_H1e zenon_H1f zenon_H100 zenon_H96 zenon_H89 zenon_H82 zenon_H95 zenon_Hd0 zenon_H4c zenon_H94 zenon_Hb4 zenon_H21 zenon_H1d. % 4.78/4.96 apply (zenon_or_s _ _ zenon_H1ee); [ zenon_intro zenon_H85 | zenon_intro zenon_H38 ]. % 4.78/4.96 apply (zenon_L350_); trivial. % 4.78/4.96 apply (zenon_L353_); trivial. % 4.78/4.96 (* end of lemma zenon_L354_ *) % 4.78/4.96 assert (zenon_L355_ : ((~((op (e2) (e1)) = (e2)))\/(~((op (e0) (e0)) = (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (e2))) -> (~((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 (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (~((e1) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (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) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (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 (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (e1))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e0) (e0)) = (e1)))) -> False). % 4.78/4.96 do 0 intro. intros zenon_H1f5 zenon_H1d zenon_H21 zenon_Hb4 zenon_H94 zenon_H4c zenon_Hd0 zenon_H95 zenon_H82 zenon_H89 zenon_H100 zenon_H1f zenon_H1e zenon_H1f4 zenon_H1f3 zenon_H1f1 zenon_H1b9 zenon_H1e8 zenon_H19d zenon_H1e7 zenon_H1bd zenon_H1e2 zenon_H1e1 zenon_H1de zenon_H1c5 zenon_H11e zenon_H1cc zenon_H1cb zenon_H1c7 zenon_H1ca zenon_H1ed zenon_H1e9 zenon_H1ec zenon_H1ee zenon_H1f0 zenon_H1ef zenon_H1f2 zenon_H1c1 zenon_H1be zenon_H1bf zenon_H1bb zenon_H1ab zenon_H1ba zenon_H19a zenon_H122 zenon_H177 zenon_H171 zenon_H154 zenon_H153 zenon_H13c zenon_H142 zenon_H13e zenon_H152 zenon_H170 zenon_H165 zenon_H166 zenon_H16b zenon_H16f zenon_H172 zenon_H173 zenon_H174 zenon_H176 zenon_H175 zenon_H28 zenon_H198 zenon_H186 zenon_H194 zenon_H18f zenon_H19b zenon_H1b6 zenon_H1c0 zenon_H1c2 zenon_H1b7 zenon_H1c3 zenon_H1c4 zenon_H114 zenon_H113 zenon_H110 zenon_He9 zenon_He6 zenon_Hdc zenon_Hda zenon_Hd7 zenon_Hdf zenon_Hbe zenon_H102 zenon_Hf6 zenon_Hef zenon_Hf3 zenon_Hf9 zenon_H101 zenon_H103 zenon_Hfd zenon_H7c zenon_H4b zenon_H46 zenon_H41 zenon_H54 zenon_H117 zenon_H86 zenon_H8f zenon_H7b zenon_H6c zenon_H70 zenon_H76 zenon_H75 zenon_He2 zenon_Hb3 zenon_Haf zenon_H9d zenon_Ha9 zenon_Ha4 zenon_Ha0 zenon_Hac zenon_Hb9 zenon_H118 zenon_H35 zenon_H36 zenon_H37 zenon_H33 zenon_H11f zenon_H12e zenon_H137 zenon_H132 zenon_H135 zenon_H19c. % 4.78/4.96 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_H96 | zenon_intro zenon_H5b ]. % 4.78/4.96 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H85 | zenon_intro zenon_H104 ]. % 4.78/4.96 apply (zenon_L350_); trivial. % 4.78/4.96 apply (zenon_L354_); trivial. % 4.78/4.96 apply (zenon_L109_); trivial. % 4.78/4.96 (* end of lemma zenon_L355_ *) % 4.78/4.96 assert (zenon_L356_ : ((op (e1) (e3)) = (e0)) -> ((op (e1) (e3)) = (e2)) -> (~((e0) = (e2))) -> False). % 4.78/4.96 do 0 intro. intros zenon_H7a zenon_Hd8 zenon_H82. % 4.78/4.96 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H83 | zenon_intro zenon_H5c ]. % 4.78/4.97 cut (((e2) = (e2)) = ((e0) = (e2))). % 4.78/4.97 intro zenon_D_pnotp. % 4.78/4.97 apply zenon_H82. % 4.78/4.97 rewrite <- zenon_D_pnotp. % 4.78/4.97 exact zenon_H83. % 4.78/4.97 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 4.78/4.97 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 4.78/4.97 congruence. % 4.78/4.97 cut (((op (e1) (e3)) = (e0)) = ((e2) = (e0))). % 4.78/4.97 intro zenon_D_pnotp. % 4.78/4.97 apply zenon_H84. % 4.78/4.97 rewrite <- zenon_D_pnotp. % 4.78/4.97 exact zenon_H7a. % 4.78/4.97 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 4.78/4.97 cut (((op (e1) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1b5]. % 4.78/4.97 congruence. % 4.78/4.97 exact (zenon_H1b5 zenon_Hd8). % 4.78/4.97 apply zenon_H52. apply refl_equal. % 4.78/4.97 apply zenon_H5c. apply refl_equal. % 4.78/4.97 apply zenon_H5c. apply refl_equal. % 4.78/4.97 (* end of lemma zenon_L356_ *) % 4.78/4.97 assert (zenon_L357_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e3)) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> False). % 4.78/4.97 do 0 intro. intros zenon_H12e zenon_H3f zenon_H82 zenon_H7a zenon_H85 zenon_H76. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H8a | zenon_intro zenon_H12f ]. % 4.78/4.97 apply (zenon_L121_); trivial. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H130 ]. % 4.78/4.97 apply (zenon_L356_); trivial. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H81 | zenon_intro zenon_H79 ]. % 4.78/4.97 exact (zenon_H85 zenon_H81). % 4.78/4.97 exact (zenon_H76 zenon_H79). % 4.78/4.97 (* end of lemma zenon_L357_ *) % 4.78/4.97 assert (zenon_L358_ : (((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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> False). % 4.78/4.97 do 0 intro. intros zenon_H33 zenon_Hc3 zenon_H36 zenon_H37 zenon_H12e zenon_H82 zenon_H7a zenon_H85 zenon_H76. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H3a | zenon_intro zenon_H39 ]. % 4.78/4.97 exact (zenon_Hc3 zenon_H3a). % 4.78/4.97 apply (zenon_or_s _ _ zenon_H39); [ zenon_intro zenon_H3e | zenon_intro zenon_H3d ]. % 4.78/4.97 exact (zenon_H36 zenon_H3e). % 4.78/4.97 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H40 | zenon_intro zenon_H3f ]. % 4.78/4.97 exact (zenon_H37 zenon_H40). % 4.78/4.97 apply (zenon_L357_); trivial. % 4.78/4.97 (* end of lemma zenon_L358_ *) % 4.78/4.97 assert (zenon_L359_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (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 (e1) (e1)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> False). % 4.78/4.97 do 0 intro. intros zenon_He9 zenon_Hbe zenon_Hbd zenon_H27 zenon_H132 zenon_H33 zenon_Hc3 zenon_H36 zenon_H37 zenon_H12e zenon_H82 zenon_H85 zenon_H76. % 4.78/4.97 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H34 | zenon_intro zenon_Hea ]. % 4.78/4.97 apply (zenon_L36_); trivial. % 4.78/4.97 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H3a | zenon_intro zenon_Heb ]. % 4.78/4.97 exact (zenon_Hc3 zenon_H3a). % 4.78/4.97 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_He5 | zenon_intro zenon_H7a ]. % 4.78/4.97 apply (zenon_L117_); trivial. % 4.78/4.97 apply (zenon_L358_); trivial. % 4.78/4.97 (* end of lemma zenon_L359_ *) % 4.78/4.97 assert (zenon_L360_ : (((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 (e0) (e3)) = (e1)) -> ((op (e2) (e3)) = (e0)) -> False). % 4.78/4.97 do 0 intro. intros zenon_H4b zenon_H179 zenon_H47 zenon_H46 zenon_H4c zenon_H87 zenon_H80. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H4b); [ zenon_intro zenon_H43 | zenon_intro zenon_H4e ]. % 4.78/4.97 exact (zenon_H179 zenon_H43). % 4.78/4.97 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H48 | zenon_intro zenon_H4f ]. % 4.78/4.97 apply (zenon_L5_); trivial. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H51 | zenon_intro zenon_H50 ]. % 4.78/4.97 exact (zenon_H4c zenon_H51). % 4.78/4.97 apply (zenon_L267_); trivial. % 4.78/4.97 (* end of lemma zenon_L360_ *) % 4.78/4.97 assert (zenon_L361_ : (~((op (e3) (op (e3) (e3))) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e1)) -> False). % 4.78/4.97 do 0 intro. intros zenon_H1f6 zenon_H72. % 4.78/4.97 cut (((op (e3) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H140]. % 4.78/4.97 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H56]. % 4.78/4.97 congruence. % 4.78/4.97 apply zenon_H56. apply refl_equal. % 4.78/4.97 exact (zenon_H140 zenon_H72). % 4.78/4.97 (* end of lemma zenon_L361_ *) % 4.78/4.97 assert (zenon_L362_ : (~((op (op (e3) (op (e3) (e3))) (op (e3) (e3))) = (op (e0) (e1)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e3) (e1)) = (e0)) -> False). % 4.78/4.97 do 0 intro. intros zenon_H1f7 zenon_H72 zenon_H10e. % 4.78/4.97 cut (((op (e3) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H140]. % 4.78/4.97 cut (((op (e3) (op (e3) (e3))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1cf]. % 4.78/4.97 congruence. % 4.78/4.97 cut (((op (e3) (e1)) = (e0)) = ((op (e3) (op (e3) (e3))) = (e0))). % 4.78/4.97 intro zenon_D_pnotp. % 4.78/4.97 apply zenon_H1cf. % 4.78/4.97 rewrite <- zenon_D_pnotp. % 4.78/4.97 exact zenon_H10e. % 4.78/4.97 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 4.78/4.97 cut (((op (e3) (e1)) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H1f8]. % 4.78/4.97 congruence. % 4.78/4.97 elim (classic ((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 4.78/4.97 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3)))) = ((op (e3) (e1)) = (op (e3) (op (e3) (e3))))). % 4.78/4.97 intro zenon_D_pnotp. % 4.78/4.97 apply zenon_H1f8. % 4.78/4.97 rewrite <- zenon_D_pnotp. % 4.78/4.97 exact zenon_H149. % 4.78/4.97 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H14a]. % 4.78/4.97 cut (((op (e3) (op (e3) (e3))) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1f6]. % 4.78/4.97 congruence. % 4.78/4.97 apply (zenon_L361_); trivial. % 4.78/4.97 apply zenon_H14a. apply refl_equal. % 4.78/4.97 apply zenon_H14a. apply refl_equal. % 4.78/4.97 apply zenon_H52. apply refl_equal. % 4.78/4.97 exact (zenon_H140 zenon_H72). % 4.78/4.97 (* end of lemma zenon_L362_ *) % 4.78/4.97 assert (zenon_L363_ : ((op (e0) (e1)) = (e2)) -> ((op (e3) (e1)) = (e0)) -> ((op (e3) (e3)) = (e1)) -> False). % 4.78/4.97 do 0 intro. intros zenon_H5e zenon_H10e zenon_H72. % 4.78/4.97 apply (zenon_notand_s _ _ ax6); [ zenon_intro zenon_H1d2 | zenon_intro zenon_H1f9 ]. % 4.78/4.97 elim (classic ((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 4.78/4.97 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3)))) = ((e0) = (op (e3) (op (e3) (e3))))). % 4.78/4.97 intro zenon_D_pnotp. % 4.78/4.97 apply zenon_H1d2. % 4.78/4.97 rewrite <- zenon_D_pnotp. % 4.78/4.97 exact zenon_H149. % 4.78/4.97 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H14a]. % 4.78/4.97 cut (((op (e3) (op (e3) (e3))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1cf]. % 4.78/4.97 congruence. % 4.78/4.97 cut (((op (e3) (e1)) = (e0)) = ((op (e3) (op (e3) (e3))) = (e0))). % 4.78/4.97 intro zenon_D_pnotp. % 4.78/4.97 apply zenon_H1cf. % 4.78/4.97 rewrite <- zenon_D_pnotp. % 4.78/4.97 exact zenon_H10e. % 4.78/4.97 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 4.78/4.97 cut (((op (e3) (e1)) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H1f8]. % 4.78/4.97 congruence. % 4.78/4.97 elim (classic ((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 4.78/4.97 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3)))) = ((op (e3) (e1)) = (op (e3) (op (e3) (e3))))). % 4.78/4.97 intro zenon_D_pnotp. % 4.78/4.97 apply zenon_H1f8. % 4.78/4.97 rewrite <- zenon_D_pnotp. % 4.78/4.97 exact zenon_H149. % 4.78/4.97 cut (((op (e3) (op (e3) (e3))) = (op (e3) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H14a]. % 4.78/4.97 cut (((op (e3) (op (e3) (e3))) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1f6]. % 4.78/4.97 congruence. % 4.78/4.97 apply (zenon_L361_); trivial. % 4.78/4.97 apply zenon_H14a. apply refl_equal. % 4.78/4.97 apply zenon_H14a. apply refl_equal. % 4.78/4.97 apply zenon_H52. apply refl_equal. % 4.78/4.97 apply zenon_H14a. apply refl_equal. % 4.78/4.97 apply zenon_H14a. apply refl_equal. % 4.78/4.97 apply (zenon_notand_s _ _ zenon_H1f9); [ zenon_intro zenon_H73 | zenon_intro zenon_H14d ]. % 4.78/4.97 apply zenon_H73. apply sym_equal. exact zenon_H72. % 4.78/4.97 elim (classic ((op (op (e3) (op (e3) (e3))) (op (e3) (e3))) = (op (op (e3) (op (e3) (e3))) (op (e3) (e3))))); [ zenon_intro zenon_H14e | zenon_intro zenon_H14f ]. % 4.78/4.97 cut (((op (op (e3) (op (e3) (e3))) (op (e3) (e3))) = (op (op (e3) (op (e3) (e3))) (op (e3) (e3)))) = ((e2) = (op (op (e3) (op (e3) (e3))) (op (e3) (e3))))). % 4.78/4.97 intro zenon_D_pnotp. % 4.78/4.97 apply zenon_H14d. % 4.78/4.97 rewrite <- zenon_D_pnotp. % 4.78/4.97 exact zenon_H14e. % 4.78/4.97 cut (((op (op (e3) (op (e3) (e3))) (op (e3) (e3))) = (op (op (e3) (op (e3) (e3))) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H14f]. % 4.78/4.97 cut (((op (op (e3) (op (e3) (e3))) (op (e3) (e3))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H150]. % 4.78/4.97 congruence. % 4.78/4.97 cut (((op (e0) (e1)) = (e2)) = ((op (op (e3) (op (e3) (e3))) (op (e3) (e3))) = (e2))). % 4.78/4.97 intro zenon_D_pnotp. % 4.78/4.97 apply zenon_H150. % 4.78/4.97 rewrite <- zenon_D_pnotp. % 4.78/4.97 exact zenon_H5e. % 4.78/4.97 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 4.78/4.97 cut (((op (e0) (e1)) = (op (op (e3) (op (e3) (e3))) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H1fa]. % 4.78/4.97 congruence. % 4.78/4.97 elim (classic ((op (op (e3) (op (e3) (e3))) (op (e3) (e3))) = (op (op (e3) (op (e3) (e3))) (op (e3) (e3))))); [ zenon_intro zenon_H14e | zenon_intro zenon_H14f ]. % 4.78/4.97 cut (((op (op (e3) (op (e3) (e3))) (op (e3) (e3))) = (op (op (e3) (op (e3) (e3))) (op (e3) (e3)))) = ((op (e0) (e1)) = (op (op (e3) (op (e3) (e3))) (op (e3) (e3))))). % 4.78/4.97 intro zenon_D_pnotp. % 4.78/4.97 apply zenon_H1fa. % 4.78/4.97 rewrite <- zenon_D_pnotp. % 4.78/4.97 exact zenon_H14e. % 4.78/4.97 cut (((op (op (e3) (op (e3) (e3))) (op (e3) (e3))) = (op (op (e3) (op (e3) (e3))) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H14f]. % 4.78/4.97 cut (((op (op (e3) (op (e3) (e3))) (op (e3) (e3))) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1f7]. % 4.78/4.97 congruence. % 4.78/4.97 apply (zenon_L362_); trivial. % 4.78/4.97 apply zenon_H14f. apply refl_equal. % 4.78/4.97 apply zenon_H14f. apply refl_equal. % 4.78/4.97 apply zenon_H5c. apply refl_equal. % 4.78/4.97 apply zenon_H14f. apply refl_equal. % 4.78/4.97 apply zenon_H14f. apply refl_equal. % 4.78/4.97 (* end of lemma zenon_L363_ *) % 4.78/4.97 assert (zenon_L364_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((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 (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e2)) -> ((op (e3) (e1)) = (e0)) -> False). % 4.78/4.97 do 0 intro. intros zenon_Hdf zenon_H80 zenon_H4c zenon_H46 zenon_H47 zenon_H179 zenon_H4b zenon_H135 zenon_H2c zenon_H76 zenon_H142 zenon_H145 zenon_H75 zenon_H5e zenon_H10e. % 4.78/4.97 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H87 | zenon_intro zenon_He0 ]. % 4.78/4.97 apply (zenon_L360_); trivial. % 4.78/4.97 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H71 | zenon_intro zenon_He1 ]. % 4.78/4.97 exact (zenon_H135 zenon_H71). % 4.78/4.97 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H72 ]. % 4.78/4.97 apply (zenon_L112_); trivial. % 4.78/4.97 apply (zenon_L363_); trivial. % 4.78/4.97 (* end of lemma zenon_L364_ *) % 4.78/4.97 assert (zenon_L365_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e2) (e3)) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((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 (e3) (e1)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> (((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)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (e1))) -> (((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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 4.78/4.97 do 0 intro. intros zenon_H117 zenon_H21 zenon_H85 zenon_H82 zenon_H12e zenon_H37 zenon_H36 zenon_Hc3 zenon_H33 zenon_H10e zenon_H5e zenon_H75 zenon_H142 zenon_H76 zenon_H2c zenon_H135 zenon_H4b zenon_H179 zenon_H47 zenon_H46 zenon_H4c zenon_Hdf zenon_H145. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H26 | zenon_intro zenon_H11a ]. % 4.78/4.97 exact (zenon_H21 zenon_H26). % 4.78/4.97 apply (zenon_or_s _ _ zenon_H11a); [ zenon_intro zenon_H7a | zenon_intro zenon_H11b ]. % 4.78/4.97 apply (zenon_L358_); trivial. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H80 | zenon_intro zenon_H6d ]. % 4.78/4.97 apply (zenon_L364_); trivial. % 4.78/4.97 exact (zenon_H145 zenon_H6d). % 4.78/4.97 (* end of lemma zenon_L365_ *) % 4.78/4.97 assert (zenon_L366_ : (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> False). % 4.78/4.97 do 0 intro. intros zenon_H1e1 zenon_H27 zenon_Hf7. % 4.78/4.97 cut (((op (e0) (e2)) = (e0)) = ((op (e0) (e2)) = (op (e3) (e2)))). % 4.78/4.97 intro zenon_D_pnotp. % 4.78/4.97 apply zenon_H1e1. % 4.78/4.97 rewrite <- zenon_D_pnotp. % 4.78/4.97 exact zenon_H27. % 4.78/4.97 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hf8]. % 4.78/4.97 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H134]. % 4.78/4.97 congruence. % 4.78/4.97 apply zenon_H134. apply refl_equal. % 4.78/4.97 apply zenon_Hf8. apply sym_equal. exact zenon_Hf7. % 4.78/4.97 (* end of lemma zenon_L366_ *) % 4.78/4.97 assert (zenon_L367_ : ((op (e0) (e3)) = (e2)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> False). % 4.78/4.97 do 0 intro. intros zenon_H8a zenon_H5e zenon_H1fb. % 4.78/4.97 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H1fc | zenon_intro zenon_H6f ]. % 4.78/4.97 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (e0) (e1)) = (op (e0) (e3)))). % 4.78/4.97 intro zenon_D_pnotp. % 4.78/4.97 apply zenon_H1fb. % 4.78/4.97 rewrite <- zenon_D_pnotp. % 4.78/4.97 exact zenon_H1fc. % 4.78/4.97 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 4.78/4.97 cut (((op (e0) (e3)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1fd]. % 4.78/4.97 congruence. % 4.78/4.97 cut (((op (e0) (e3)) = (e2)) = ((op (e0) (e3)) = (op (e0) (e1)))). % 4.78/4.97 intro zenon_D_pnotp. % 4.78/4.97 apply zenon_H1fd. % 4.78/4.97 rewrite <- zenon_D_pnotp. % 4.78/4.97 exact zenon_H8a. % 4.78/4.97 cut (((e2) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1fe]. % 4.78/4.97 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 4.78/4.97 congruence. % 4.78/4.97 apply zenon_H6f. apply refl_equal. % 4.78/4.97 apply zenon_H1fe. apply sym_equal. exact zenon_H5e. % 4.78/4.97 apply zenon_H6f. apply refl_equal. % 4.78/4.97 apply zenon_H6f. apply refl_equal. % 4.78/4.97 (* end of lemma zenon_L367_ *) % 4.78/4.97 assert (zenon_L368_ : (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e3)) -> ((op (e1) (e1)) = (e3)) -> False). % 4.78/4.97 do 0 intro. intros zenon_H19d zenon_Hd1 zenon_H3f. % 4.78/4.97 cut (((op (e0) (e1)) = (e3)) = ((op (e0) (e1)) = (op (e1) (e1)))). % 4.78/4.97 intro zenon_D_pnotp. % 4.78/4.97 apply zenon_H19d. % 4.78/4.97 rewrite <- zenon_D_pnotp. % 4.78/4.97 exact zenon_Hd1. % 4.78/4.97 cut (((e3) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H15e]. % 4.78/4.97 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hd3]. % 4.78/4.97 congruence. % 4.78/4.97 apply zenon_Hd3. apply refl_equal. % 4.78/4.97 apply zenon_H15e. apply sym_equal. exact zenon_H3f. % 4.78/4.97 (* end of lemma zenon_L368_ *) % 4.78/4.97 assert (zenon_L369_ : (((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)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e3)) -> False). % 4.78/4.97 do 0 intro. intros zenon_H33 zenon_Hc3 zenon_H36 zenon_H37 zenon_H19d zenon_Hd1. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H3a | zenon_intro zenon_H39 ]. % 4.78/4.97 exact (zenon_Hc3 zenon_H3a). % 4.78/4.97 apply (zenon_or_s _ _ zenon_H39); [ zenon_intro zenon_H3e | zenon_intro zenon_H3d ]. % 4.78/4.97 exact (zenon_H36 zenon_H3e). % 4.78/4.97 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H40 | zenon_intro zenon_H3f ]. % 4.78/4.97 exact (zenon_H37 zenon_H40). % 4.78/4.97 apply (zenon_L368_); trivial. % 4.78/4.97 (* end of lemma zenon_L369_ *) % 4.78/4.97 assert (zenon_L370_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e3)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 4.78/4.97 do 0 intro. intros zenon_H117 zenon_H21 zenon_H76 zenon_H85 zenon_H82 zenon_H3f zenon_H12e zenon_H87 zenon_H4c zenon_H46 zenon_H47 zenon_H179 zenon_H4b zenon_H145. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H26 | zenon_intro zenon_H11a ]. % 4.78/4.97 exact (zenon_H21 zenon_H26). % 4.78/4.97 apply (zenon_or_s _ _ zenon_H11a); [ zenon_intro zenon_H7a | zenon_intro zenon_H11b ]. % 4.78/4.97 apply (zenon_L357_); trivial. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H80 | zenon_intro zenon_H6d ]. % 4.78/4.97 apply (zenon_L360_); trivial. % 4.78/4.97 exact (zenon_H145 zenon_H6d). % 4.78/4.97 (* end of lemma zenon_L370_ *) % 4.78/4.97 assert (zenon_L371_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 4.78/4.97 do 0 intro. intros zenon_H75 zenon_H145 zenon_Hd5 zenon_H142 zenon_H8a zenon_H6c zenon_H2c. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H75); [ zenon_intro zenon_H6d | zenon_intro zenon_H77 ]. % 4.78/4.97 exact (zenon_H145 zenon_H6d). % 4.78/4.97 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H72 | zenon_intro zenon_H78 ]. % 4.78/4.97 apply (zenon_L111_); trivial. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H79 | zenon_intro zenon_H31 ]. % 4.78/4.97 apply (zenon_L251_); trivial. % 4.78/4.97 exact (zenon_H2c zenon_H31). % 4.78/4.97 (* end of lemma zenon_L371_ *) % 4.78/4.97 assert (zenon_L372_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 4.78/4.97 do 0 intro. intros zenon_H16b zenon_H9d zenon_H98 zenon_H9c zenon_Hd0 zenon_H47 zenon_H46 zenon_H75 zenon_H145 zenon_H142 zenon_H8a zenon_H6c zenon_H2c. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H16d ]. % 4.78/4.97 apply (zenon_L75_); trivial. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H16e ]. % 4.78/4.97 apply (zenon_L127_); trivial. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_H48 | zenon_intro zenon_Hd5 ]. % 4.78/4.97 apply (zenon_L5_); trivial. % 4.78/4.97 apply (zenon_L371_); trivial. % 4.78/4.97 (* end of lemma zenon_L372_ *) % 4.78/4.97 assert (zenon_L373_ : (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e1)) -> ((op (e3) (e1)) = (e0)) -> (((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)) = (op (e1) (e1)))) -> False). % 4.78/4.97 do 0 intro. intros zenon_H1ff zenon_H1f zenon_H2c zenon_H6c zenon_H8a zenon_H142 zenon_H145 zenon_H75 zenon_H46 zenon_H47 zenon_Hd0 zenon_H98 zenon_H9d zenon_H16b zenon_H72 zenon_H10e zenon_H33 zenon_Hc3 zenon_H36 zenon_H37 zenon_H19d. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 4.78/4.97 exact (zenon_H1f zenon_H25). % 4.78/4.97 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H9c | zenon_intro zenon_H201 ]. % 4.78/4.97 apply (zenon_L372_); trivial. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H5e | zenon_intro zenon_Hd1 ]. % 4.78/4.97 apply (zenon_L363_); trivial. % 4.78/4.97 apply (zenon_L369_); trivial. % 4.78/4.97 (* end of lemma zenon_L373_ *) % 4.78/4.97 assert (zenon_L374_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((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 (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e3)) -> (~((e0) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e1)) = (e0)) -> (((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)) = (op (e1) (e1)))) -> False). % 4.78/4.97 do 0 intro. intros zenon_Hdf zenon_H4b zenon_H179 zenon_H4c zenon_H12e zenon_H3f zenon_H82 zenon_H85 zenon_H21 zenon_H117 zenon_H135 zenon_H76 zenon_H1ff zenon_H1f zenon_H2c zenon_H6c zenon_H8a zenon_H142 zenon_H145 zenon_H75 zenon_H46 zenon_H47 zenon_Hd0 zenon_H98 zenon_H9d zenon_H16b zenon_H10e zenon_H33 zenon_Hc3 zenon_H36 zenon_H37 zenon_H19d. % 4.78/4.97 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H87 | zenon_intro zenon_He0 ]. % 4.78/4.97 apply (zenon_L370_); trivial. % 4.78/4.97 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H71 | zenon_intro zenon_He1 ]. % 4.78/4.97 exact (zenon_H135 zenon_H71). % 4.78/4.97 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H72 ]. % 4.78/4.97 apply (zenon_L112_); trivial. % 4.78/4.97 apply (zenon_L373_); trivial. % 4.78/4.97 (* end of lemma zenon_L374_ *) % 4.78/4.97 assert (zenon_L375_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 4.78/4.97 do 0 intro. intros zenon_H75 zenon_H145 zenon_Hd5 zenon_H142 zenon_Ha5 zenon_Hf9 zenon_H2c. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H75); [ zenon_intro zenon_H6d | zenon_intro zenon_H77 ]. % 4.78/4.97 exact (zenon_H145 zenon_H6d). % 4.78/4.97 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H72 | zenon_intro zenon_H78 ]. % 4.78/4.97 apply (zenon_L111_); trivial. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H79 | zenon_intro zenon_H31 ]. % 4.78/4.97 apply (zenon_L175_); trivial. % 4.78/4.97 exact (zenon_H2c zenon_H31). % 4.78/4.97 (* end of lemma zenon_L375_ *) % 4.78/4.97 assert (zenon_L376_ : (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e1)) -> ((op (e3) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e3)) -> False). % 4.78/4.97 do 0 intro. intros zenon_H1ff zenon_H1f zenon_H2c zenon_H6c zenon_H8a zenon_H142 zenon_H145 zenon_H75 zenon_H46 zenon_H47 zenon_H98 zenon_H9d zenon_H16b zenon_H72 zenon_H10e zenon_Hd0 zenon_H5d. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H1ff); [ zenon_intro zenon_H25 | zenon_intro zenon_H200 ]. % 4.78/4.97 exact (zenon_H1f zenon_H25). % 4.78/4.97 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H9c | zenon_intro zenon_H201 ]. % 4.78/4.97 apply (zenon_L372_); trivial. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H5e | zenon_intro zenon_Hd1 ]. % 4.78/4.97 apply (zenon_L363_); trivial. % 4.78/4.97 apply (zenon_L39_); trivial. % 4.78/4.97 (* end of lemma zenon_L376_ *) % 4.78/4.97 assert (zenon_L377_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (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 (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e2)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e3)) -> False). % 4.78/4.97 do 0 intro. intros zenon_Hdf zenon_H80 zenon_H4c zenon_H179 zenon_H4b zenon_H135 zenon_Hf9 zenon_Ha5 zenon_H1ff zenon_H1f zenon_H2c zenon_H6c zenon_H8a zenon_H142 zenon_H145 zenon_H75 zenon_H46 zenon_H47 zenon_H98 zenon_H9d zenon_H16b zenon_H10e zenon_Hd0 zenon_H5d. % 4.78/4.97 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H87 | zenon_intro zenon_He0 ]. % 4.78/4.97 apply (zenon_L360_); trivial. % 4.78/4.97 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H71 | zenon_intro zenon_He1 ]. % 4.78/4.97 exact (zenon_H135 zenon_H71). % 4.78/4.97 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H72 ]. % 4.78/4.97 apply (zenon_L375_); trivial. % 4.78/4.97 apply (zenon_L376_); trivial. % 4.78/4.97 (* end of lemma zenon_L377_ *) % 4.78/4.97 assert (zenon_L378_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((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) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e1)) = (e0)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (e1))) -> (((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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 4.78/4.97 do 0 intro. intros zenon_H117 zenon_H21 zenon_H76 zenon_H85 zenon_H82 zenon_H12e zenon_H37 zenon_H36 zenon_Hc3 zenon_H33 zenon_H5d zenon_Hd0 zenon_H10e zenon_H16b zenon_H9d zenon_H98 zenon_H47 zenon_H46 zenon_H75 zenon_H142 zenon_H8a zenon_H6c zenon_H2c zenon_H1f zenon_H1ff zenon_Ha5 zenon_Hf9 zenon_H135 zenon_H4b zenon_H179 zenon_H4c zenon_Hdf zenon_H145. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H26 | zenon_intro zenon_H11a ]. % 4.78/4.97 exact (zenon_H21 zenon_H26). % 4.78/4.97 apply (zenon_or_s _ _ zenon_H11a); [ zenon_intro zenon_H7a | zenon_intro zenon_H11b ]. % 4.78/4.97 apply (zenon_L358_); trivial. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H80 | zenon_intro zenon_H6d ]. % 4.78/4.97 apply (zenon_L377_); trivial. % 4.78/4.97 exact (zenon_H145 zenon_H6d). % 4.78/4.97 (* end of lemma zenon_L378_ *) % 4.78/4.97 assert (zenon_L379_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((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 (e0) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e1)) = (e0)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e3)) = (e1))) -> False). % 4.78/4.97 do 0 intro. intros zenon_H7b zenon_Hb9 zenon_H34 zenon_H2a zenon_H117 zenon_H21 zenon_H76 zenon_H85 zenon_H82 zenon_H12e zenon_H37 zenon_H36 zenon_Hc3 zenon_H33 zenon_Hd0 zenon_H10e zenon_H16b zenon_H9d zenon_H98 zenon_H46 zenon_H75 zenon_H142 zenon_H8a zenon_H6c zenon_H2c zenon_H1f zenon_H1ff zenon_Hf9 zenon_H4b zenon_H179 zenon_H4c zenon_Hdf zenon_H145 zenon_H19d zenon_H202 zenon_H96 zenon_H1fb zenon_Hac zenon_H135. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H7b); [ zenon_intro zenon_H7e | zenon_intro zenon_H7d ]. % 4.78/4.97 apply (zenon_L110_); trivial. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H7d); [ zenon_intro zenon_H3e | zenon_intro zenon_H7f ]. % 4.78/4.97 exact (zenon_H36 zenon_H3e). % 4.78/4.97 apply (zenon_or_s _ _ zenon_H7f); [ zenon_intro zenon_H47 | zenon_intro zenon_H71 ]. % 4.78/4.97 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H5e | zenon_intro zenon_Had ]. % 4.78/4.97 apply (zenon_L367_); trivial. % 4.78/4.97 apply (zenon_or_s _ _ zenon_Had); [ zenon_intro zenon_H40 | zenon_intro zenon_Hae ]. % 4.78/4.97 exact (zenon_H37 zenon_H40). % 4.78/4.97 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 4.78/4.97 exact (zenon_H96 zenon_H9a). % 4.78/4.97 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H203 ]. % 4.78/4.97 apply (zenon_L369_); trivial. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H3f | zenon_intro zenon_H204 ]. % 4.78/4.97 apply (zenon_L374_); trivial. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H5d | zenon_intro zenon_H30 ]. % 4.78/4.97 apply (zenon_L378_); trivial. % 4.78/4.97 exact (zenon_H2a zenon_H30). % 4.78/4.97 exact (zenon_H135 zenon_H71). % 4.78/4.97 (* end of lemma zenon_L379_ *) % 4.78/4.97 assert (zenon_L380_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> False). % 4.78/4.97 do 0 intro. intros zenon_H94 zenon_H205 zenon_Hb0 zenon_H96 zenon_H4c zenon_H85. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H98 | zenon_intro zenon_H97 ]. % 4.78/4.97 elim (classic ((op (e3) (e0)) = (op (e3) (e0)))); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hb2 ]. % 4.78/4.97 cut (((op (e3) (e0)) = (op (e3) (e0))) = ((op (e2) (e0)) = (op (e3) (e0)))). % 4.78/4.97 intro zenon_D_pnotp. % 4.78/4.97 apply zenon_H205. % 4.78/4.97 rewrite <- zenon_D_pnotp. % 4.78/4.97 exact zenon_Hbf. % 4.78/4.97 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 4.78/4.97 cut (((op (e3) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H206]. % 4.78/4.97 congruence. % 4.78/4.97 cut (((op (e3) (e0)) = (e2)) = ((op (e3) (e0)) = (op (e2) (e0)))). % 4.78/4.97 intro zenon_D_pnotp. % 4.78/4.97 apply zenon_H206. % 4.78/4.97 rewrite <- zenon_D_pnotp. % 4.78/4.97 exact zenon_Hb0. % 4.78/4.97 cut (((e2) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H207]. % 4.78/4.97 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 4.78/4.97 congruence. % 4.78/4.97 apply zenon_Hb2. apply refl_equal. % 4.78/4.97 apply zenon_H207. apply sym_equal. exact zenon_H98. % 4.78/4.97 apply zenon_Hb2. apply refl_equal. % 4.78/4.97 apply zenon_Hb2. apply refl_equal. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H9a | zenon_intro zenon_H99 ]. % 4.78/4.97 exact (zenon_H96 zenon_H9a). % 4.78/4.97 apply (zenon_or_s _ _ zenon_H99); [ zenon_intro zenon_H51 | zenon_intro zenon_H81 ]. % 4.78/4.97 exact (zenon_H4c zenon_H51). % 4.78/4.97 exact (zenon_H85 zenon_H81). % 4.78/4.97 (* end of lemma zenon_L380_ *) % 4.78/4.97 assert (zenon_L381_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (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 (e1) (e1)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> False). % 4.78/4.97 do 0 intro. intros zenon_He9 zenon_H1ab zenon_H42 zenon_H27 zenon_H132 zenon_H33 zenon_Hc3 zenon_H36 zenon_H37 zenon_H12e zenon_H82 zenon_H85 zenon_H76. % 4.78/4.97 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H34 | zenon_intro zenon_Hea ]. % 4.78/4.97 apply (zenon_L179_); trivial. % 4.78/4.97 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H3a | zenon_intro zenon_Heb ]. % 4.78/4.97 exact (zenon_Hc3 zenon_H3a). % 4.78/4.97 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_He5 | zenon_intro zenon_H7a ]. % 4.78/4.97 apply (zenon_L117_); trivial. % 4.78/4.97 apply (zenon_L358_); trivial. % 4.78/4.97 (* end of lemma zenon_L381_ *) % 4.78/4.97 assert (zenon_L382_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e2)) -> ((op (e3) (e1)) = (e0)) -> False). % 4.78/4.97 do 0 intro. intros zenon_Hdf zenon_H13c zenon_H8c zenon_H135 zenon_H2c zenon_H76 zenon_H142 zenon_H145 zenon_H75 zenon_H5e zenon_H10e. % 4.78/4.97 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H87 | zenon_intro zenon_He0 ]. % 4.78/4.97 apply (zenon_L95_); trivial. % 4.78/4.97 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H71 | zenon_intro zenon_He1 ]. % 4.78/4.97 exact (zenon_H135 zenon_H71). % 4.78/4.97 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H72 ]. % 4.78/4.97 apply (zenon_L112_); trivial. % 4.78/4.97 apply (zenon_L363_); trivial. % 4.78/4.97 (* end of lemma zenon_L382_ *) % 4.78/4.97 assert (zenon_L383_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e3)) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((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 (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e2)) -> (((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)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (e1))) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> False). % 4.78/4.97 do 0 intro. intros zenon_H1de zenon_H85 zenon_H82 zenon_H12e zenon_H37 zenon_H36 zenon_Hc3 zenon_H33 zenon_H132 zenon_Hbe zenon_He9 zenon_H5e zenon_H75 zenon_H142 zenon_H76 zenon_H2c zenon_H135 zenon_H8c zenon_H13c zenon_Hdf zenon_H27 zenon_H1e1 zenon_H145. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H1de); [ zenon_intro zenon_Hbd | zenon_intro zenon_H1df ]. % 4.78/4.97 apply (zenon_L359_); trivial. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_H10e | zenon_intro zenon_H1e0 ]. % 4.78/4.97 apply (zenon_L382_); trivial. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H6d ]. % 4.78/4.97 apply (zenon_L366_); trivial. % 4.78/4.97 exact (zenon_H145 zenon_H6d). % 4.78/4.97 (* end of lemma zenon_L383_ *) % 4.78/4.97 assert (zenon_L384_ : ((~((op (e1) (e1)) = (e1)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (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)))) -> (((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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((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) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (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)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> False). % 4.78/4.97 do 0 intro. intros zenon_H1b8 zenon_H174 zenon_H173 zenon_H171 zenon_H154 zenon_H153 zenon_H103 zenon_H13c zenon_Hfd zenon_H54 zenon_H113 zenon_H75 zenon_H70 zenon_H142 zenon_H117 zenon_H13e zenon_Hdf zenon_H1d zenon_H118 zenon_H11f zenon_H76 zenon_H12e zenon_Hb9 zenon_Hb3 zenon_Haf zenon_H9d zenon_Ha9 zenon_Ha4 zenon_H4c zenon_Ha0 zenon_H82 zenon_Hac zenon_Hb4 zenon_H137 zenon_H94 zenon_Hd0 zenon_H100 zenon_H132 zenon_H7b zenon_H114 zenon_H1f zenon_H1e zenon_H152 zenon_H170 zenon_Hbe zenon_H165 zenon_H86 zenon_H166 zenon_He9 zenon_H16b zenon_H16f zenon_H172 zenon_H1b7 zenon_H122 zenon_Hc3 zenon_H37 zenon_H38 zenon_H33. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H1b8); [ zenon_intro zenon_H36 | zenon_intro zenon_H5b ]. % 4.78/4.97 apply (zenon_L189_); trivial. % 4.78/4.97 apply (zenon_L208_); trivial. % 4.78/4.97 (* end of lemma zenon_L384_ *) % 4.78/4.97 assert (zenon_L385_ : ((~((op (e2) (e1)) = (e2)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e0) (e0)) = (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((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 (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((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)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (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 (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e1) (e1)) = (e1)))) -> False). % 4.78/4.97 do 0 intro. intros zenon_H1f5 zenon_H19c zenon_H132 zenon_H137 zenon_H12e zenon_H11f zenon_H21 zenon_H1d zenon_H33 zenon_H38 zenon_H37 zenon_H36 zenon_H35 zenon_H118 zenon_Hb9 zenon_Hac zenon_Ha0 zenon_Ha4 zenon_Ha9 zenon_H9d zenon_Haf zenon_Hb3 zenon_Hb4 zenon_He2 zenon_H75 zenon_H76 zenon_H70 zenon_H6c zenon_H7b zenon_H82 zenon_H8f zenon_H89 zenon_H86 zenon_H117 zenon_H54 zenon_H94 zenon_H41 zenon_H46 zenon_H4c zenon_H4d zenon_H4b zenon_H7c zenon_H100 zenon_Hfd zenon_H103 zenon_H101 zenon_Hf9 zenon_Hf3 zenon_Hef zenon_Hf6 zenon_H102 zenon_Hbe zenon_Hd0 zenon_Hdf zenon_Hd7 zenon_Hda zenon_Hdc zenon_He6 zenon_He9 zenon_H104 zenon_H110 zenon_H113 zenon_H114 zenon_H1f zenon_H1e zenon_H1c4 zenon_H1c3 zenon_H1b7 zenon_H1c2 zenon_H1c0 zenon_H1b6 zenon_H19b zenon_H18f zenon_H194 zenon_H186 zenon_H198 zenon_H28 zenon_H175 zenon_H176 zenon_H174 zenon_H173 zenon_H172 zenon_H16f zenon_H16b zenon_H166 zenon_H165 zenon_H170 zenon_H152 zenon_H13e zenon_H142 zenon_H13c zenon_H153 zenon_H154 zenon_H171 zenon_H177 zenon_H122 zenon_H19a zenon_H1ba zenon_H1ab zenon_H1bb zenon_H1bf zenon_H1be zenon_H1c1 zenon_H1f2 zenon_H1ef zenon_H1f0 zenon_H1ee zenon_H1ec zenon_H1e9 zenon_H1ed zenon_H1ca zenon_H1c7 zenon_H1cb zenon_H1cc zenon_H11e zenon_H1c5 zenon_H1de zenon_H1e1 zenon_H1e2 zenon_H1bd zenon_H1e7 zenon_H19d zenon_H1e8 zenon_H1b9 zenon_H1f1 zenon_H1f3 zenon_H1f4. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H1f1); [ zenon_intro zenon_H135 | zenon_intro zenon_H2c ]. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H95 | zenon_intro zenon_Hc3 ]. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_H96 | zenon_intro zenon_H5b ]. % 4.78/4.97 apply (zenon_L352_); trivial. % 4.78/4.97 apply (zenon_L109_); trivial. % 4.78/4.97 apply (zenon_L189_); trivial. % 4.78/4.97 apply (zenon_L346_); trivial. % 4.78/4.97 (* end of lemma zenon_L385_ *) % 4.78/4.97 assert (zenon_L386_ : ((~((op (e2) (e1)) = (e2)))\/(~((op (e0) (e0)) = (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((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 (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (~((e1) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (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) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (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 (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (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 (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e0) (e0)) = (e1)))) -> False). % 4.78/4.97 do 0 intro. intros zenon_H1f5 zenon_H1d zenon_H21 zenon_Hb4 zenon_H94 zenon_H4c zenon_Hd0 zenon_H82 zenon_H89 zenon_H100 zenon_H1f zenon_H1e zenon_H1f4 zenon_H1f3 zenon_H1f1 zenon_H1b9 zenon_H1e8 zenon_H19d zenon_H1e7 zenon_H1bd zenon_H1e2 zenon_H1e1 zenon_H1de zenon_H1c5 zenon_H11e zenon_H1cc zenon_H1cb zenon_H1c7 zenon_H1ca zenon_H1ed zenon_H1e9 zenon_H1ec zenon_H1ee zenon_H1f0 zenon_H1ef zenon_H1f2 zenon_H1c1 zenon_H1be zenon_H1bf zenon_H1bb zenon_H1ab zenon_H1ba zenon_H19a zenon_H122 zenon_H177 zenon_H171 zenon_H154 zenon_H153 zenon_H13c zenon_H142 zenon_H13e zenon_H152 zenon_H170 zenon_H165 zenon_H166 zenon_H16b zenon_H16f zenon_H172 zenon_H173 zenon_H174 zenon_H176 zenon_H175 zenon_H28 zenon_H198 zenon_H186 zenon_H194 zenon_H18f zenon_H19b zenon_H1b6 zenon_H1c0 zenon_H1c2 zenon_H1b7 zenon_H1c3 zenon_H1c4 zenon_H114 zenon_H113 zenon_H110 zenon_H104 zenon_He9 zenon_He6 zenon_Hdc zenon_Hda zenon_Hd7 zenon_Hdf zenon_Hbe zenon_H102 zenon_Hf6 zenon_Hef zenon_Hf3 zenon_Hf9 zenon_H101 zenon_H103 zenon_Hfd zenon_H7c zenon_H4b zenon_H46 zenon_H41 zenon_H54 zenon_H117 zenon_H86 zenon_H8f zenon_H7b zenon_H6c zenon_H70 zenon_H76 zenon_H75 zenon_He2 zenon_Hb3 zenon_Haf zenon_H9d zenon_Ha9 zenon_Ha4 zenon_Ha0 zenon_Hac zenon_Hb9 zenon_H118 zenon_H35 zenon_H36 zenon_H37 zenon_H38 zenon_H33 zenon_H11f zenon_H12e zenon_H137 zenon_H132 zenon_H19c. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H135 | zenon_intro zenon_H4d ]. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H95 | zenon_intro zenon_Hc3 ]. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_H96 | zenon_intro zenon_H5b ]. % 4.78/4.97 apply (zenon_L353_); trivial. % 4.78/4.97 apply (zenon_L109_); trivial. % 4.78/4.97 apply (zenon_L189_); trivial. % 4.78/4.97 apply (zenon_L385_); trivial. % 4.78/4.97 (* end of lemma zenon_L386_ *) % 4.78/4.97 assert (zenon_L387_ : ((~((op (e1) (e1)) = (e1)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e0) (e0)) = (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((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 (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((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)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e1) (e1)) = (e1)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e0) (e0)) = (e1)))) -> False). % 4.78/4.97 do 0 intro. intros zenon_H1b8 zenon_H19c zenon_H132 zenon_H137 zenon_H12e zenon_H11f zenon_H33 zenon_H38 zenon_H37 zenon_H35 zenon_H118 zenon_Hb9 zenon_Hac zenon_Ha0 zenon_Ha4 zenon_Ha9 zenon_H9d zenon_Haf zenon_Hb3 zenon_He2 zenon_H75 zenon_H76 zenon_H70 zenon_H6c zenon_H7b zenon_H8f zenon_H86 zenon_H117 zenon_H54 zenon_H41 zenon_H46 zenon_H4b zenon_Hfd zenon_H103 zenon_H101 zenon_Hf9 zenon_Hf3 zenon_Hef zenon_Hf6 zenon_H102 zenon_Hbe zenon_Hdf zenon_Hd7 zenon_Hda zenon_Hdc zenon_He6 zenon_He9 zenon_H104 zenon_H110 zenon_H113 zenon_H114 zenon_H1c4 zenon_H1c3 zenon_H1b7 zenon_H1c2 zenon_H1c0 zenon_H1b6 zenon_H19b zenon_H18f zenon_H194 zenon_H186 zenon_H198 zenon_H28 zenon_H175 zenon_H176 zenon_H174 zenon_H173 zenon_H172 zenon_H16f zenon_H16b zenon_H166 zenon_H165 zenon_H170 zenon_H152 zenon_H13e zenon_H142 zenon_H13c zenon_H153 zenon_H154 zenon_H171 zenon_H177 zenon_H122 zenon_H19a zenon_H1ba zenon_H1ab zenon_H1bb zenon_H1bf zenon_H1be zenon_H1c1 zenon_H1f2 zenon_H1ef zenon_H1f0 zenon_H1ee zenon_H1ec zenon_H1e9 zenon_H1ed zenon_H1ca zenon_H1c7 zenon_H1cb zenon_H1cc zenon_H11e zenon_H1c5 zenon_H1de zenon_H1e1 zenon_H1e2 zenon_H1bd zenon_H1e7 zenon_H19d zenon_H1e8 zenon_H1b9 zenon_H1f1 zenon_H1f3 zenon_H1f4 zenon_H1e zenon_H1f zenon_H100 zenon_H89 zenon_H82 zenon_Hd0 zenon_H4c zenon_H94 zenon_Hb4 zenon_H1d zenon_H1f5. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H1c2); [ zenon_intro zenon_H21 | zenon_intro zenon_H4d ]. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H7c | zenon_intro zenon_Hc3 ]. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H1b8); [ zenon_intro zenon_H36 | zenon_intro zenon_H5b ]. % 4.78/4.97 apply (zenon_L386_); trivial. % 4.78/4.97 apply (zenon_L344_); trivial. % 4.78/4.97 apply (zenon_L384_); trivial. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H1be); [ zenon_intro zenon_H21 | zenon_intro zenon_H2c ]. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H7c | zenon_intro zenon_Hc3 ]. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H1b8); [ zenon_intro zenon_H36 | zenon_intro zenon_H5b ]. % 4.78/4.97 apply (zenon_L385_); trivial. % 4.78/4.97 apply (zenon_L207_); trivial. % 4.78/4.97 apply (zenon_L384_); trivial. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H7c | zenon_intro zenon_Hc3 ]. % 4.78/4.97 apply (zenon_L347_); trivial. % 4.78/4.97 apply (zenon_L384_); trivial. % 4.78/4.97 (* end of lemma zenon_L387_ *) % 4.78/4.97 assert (zenon_L388_ : ((~((op (e2) (e1)) = (e2)))\/(~((op (e0) (e0)) = (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (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) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e0) (e0)) = (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (e1))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((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 (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (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 (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> False). % 4.78/4.97 do 0 intro. intros zenon_H1f5 zenon_H89 zenon_H1f4 zenon_H1f3 zenon_H1f1 zenon_H1b9 zenon_H1e7 zenon_H1bd zenon_H1e2 zenon_H1c5 zenon_H11e zenon_H1cc zenon_H1cb zenon_H1c7 zenon_H1ca zenon_H1ed zenon_H1e9 zenon_H1ec zenon_H1ee zenon_H1f0 zenon_H1ef zenon_H1f2 zenon_H1c1 zenon_H1be zenon_H1bf zenon_H1bb zenon_H1ab zenon_H1ba zenon_H19a zenon_H177 zenon_H176 zenon_H175 zenon_H28 zenon_H198 zenon_H186 zenon_H194 zenon_H18f zenon_H19b zenon_H1b6 zenon_H1c0 zenon_H1c2 zenon_H1c3 zenon_H1c4 zenon_H110 zenon_He6 zenon_Hdc zenon_Hda zenon_Hd7 zenon_H102 zenon_Hf6 zenon_Hef zenon_Hf3 zenon_Hf9 zenon_H101 zenon_H4b zenon_H46 zenon_H41 zenon_H8f zenon_H6c zenon_He2 zenon_H35 zenon_H19c zenon_H1d zenon_H21 zenon_Hb4 zenon_H103 zenon_He9 zenon_H12e zenon_H76 zenon_H82 zenon_H132 zenon_Hbe zenon_Hdf zenon_H145 zenon_H142 zenon_H75 zenon_H135 zenon_H13c zenon_H1e1 zenon_H1de zenon_H54 zenon_Hc3 zenon_H36 zenon_H37 zenon_H19d zenon_H33 zenon_H104 zenon_Hfd zenon_H100 zenon_H1f zenon_H1e zenon_H1b8 zenon_H174 zenon_H173 zenon_H171 zenon_H154 zenon_H153 zenon_H113 zenon_H70 zenon_H117 zenon_H13e zenon_H118 zenon_H11f zenon_Hb9 zenon_Hb3 zenon_Haf zenon_H9d zenon_Ha9 zenon_Ha4 zenon_H4c zenon_Ha0 zenon_Hac zenon_H137 zenon_H94 zenon_Hd0 zenon_H7b zenon_H114 zenon_H152 zenon_H170 zenon_H165 zenon_H86 zenon_H166 zenon_H16b zenon_H16f zenon_H172 zenon_H1b7 zenon_H122 zenon_H1e8. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H1ee); [ zenon_intro zenon_H85 | zenon_intro zenon_H38 ]. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H1e8); [ zenon_intro zenon_H2c | zenon_intro zenon_H38 ]. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ]. % 4.78/4.97 exact (zenon_H1e zenon_H23). % 4.78/4.97 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ]. % 4.78/4.97 exact (zenon_H1f zenon_H25). % 4.78/4.97 apply (zenon_or_s _ _ zenon_H24); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hb6 | zenon_intro zenon_H105 ]. % 4.78/4.97 exact (zenon_Hb4 zenon_Hb6). % 4.78/4.97 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H5e | zenon_intro zenon_H106 ]. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_H108 | zenon_intro zenon_H107 ]. % 4.78/4.97 exact (zenon_H104 zenon_H108). % 4.78/4.97 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H109 ]. % 4.78/4.97 apply (zenon_L369_); trivial. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Hed | zenon_intro zenon_H8c ]. % 4.78/4.97 apply (zenon_L53_); trivial. % 4.78/4.97 apply (zenon_L383_); trivial. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_H92 | zenon_intro zenon_H8a ]. % 4.78/4.97 apply (zenon_L23_); trivial. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_H108 | zenon_intro zenon_H107 ]. % 4.78/4.97 exact (zenon_H104 zenon_H108). % 4.78/4.97 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H109 ]. % 4.78/4.97 apply (zenon_L369_); trivial. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_Hed | zenon_intro zenon_H8c ]. % 4.78/4.97 apply (zenon_L53_); trivial. % 4.78/4.97 apply (zenon_L115_); trivial. % 4.78/4.97 exact (zenon_H21 zenon_H26). % 4.78/4.97 apply (zenon_L384_); trivial. % 4.78/4.97 apply (zenon_L387_); trivial. % 4.78/4.97 (* end of lemma zenon_L388_ *) % 4.78/4.97 assert (zenon_L389_ : ((~((op (e2) (e1)) = (e2)))\/(~((op (e0) (e0)) = (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (e2))) -> (~((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 (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e0) (e0)) = (e1)))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((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)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (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 (e1) (e0)) = (e1))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e1) (e1)) = (e1)))) -> False). % 4.78/4.97 do 0 intro. intros zenon_H1f5 zenon_H1d zenon_H21 zenon_Hb4 zenon_H94 zenon_H4c zenon_Hd0 zenon_H95 zenon_H82 zenon_H89 zenon_H100 zenon_H1f zenon_H1e zenon_H19c zenon_H135 zenon_H132 zenon_H137 zenon_H12e zenon_H11f zenon_H33 zenon_H37 zenon_H36 zenon_H35 zenon_H118 zenon_Hb9 zenon_Hac zenon_Ha0 zenon_Ha4 zenon_Ha9 zenon_H9d zenon_Haf zenon_Hb3 zenon_He2 zenon_H75 zenon_H76 zenon_H70 zenon_H6c zenon_H7b zenon_H8f zenon_H86 zenon_H117 zenon_H54 zenon_H41 zenon_H46 zenon_H4b zenon_H7c zenon_Hfd zenon_H103 zenon_H101 zenon_Hf9 zenon_Hf3 zenon_Hef zenon_Hf6 zenon_H102 zenon_Hbe zenon_Hdf zenon_Hd7 zenon_Hda zenon_Hdc zenon_He6 zenon_He9 zenon_H104 zenon_H110 zenon_H113 zenon_H114 zenon_H1c4 zenon_H1c3 zenon_H1b7 zenon_H1c2 zenon_H1c0 zenon_H1b6 zenon_H19b zenon_H18f zenon_H194 zenon_H186 zenon_H198 zenon_H28 zenon_H175 zenon_H176 zenon_H174 zenon_H173 zenon_H172 zenon_H16f zenon_H16b zenon_H166 zenon_H165 zenon_H170 zenon_H152 zenon_H13e zenon_H142 zenon_H13c zenon_H153 zenon_H154 zenon_H171 zenon_H177 zenon_H122 zenon_H19a zenon_H1ba zenon_H1ab zenon_H1bb zenon_H1bf zenon_H1be zenon_H1c1 zenon_H1f2 zenon_H1ef zenon_H1f0 zenon_H1ee zenon_H1ec zenon_H1e9 zenon_H1ed zenon_H1ca zenon_H1c7 zenon_H1cb zenon_H1cc zenon_H11e zenon_H1c5 zenon_H1de zenon_H1e1 zenon_H1e2 zenon_H1bd zenon_H1e7 zenon_H19d zenon_H1e8 zenon_H1b9 zenon_H1f1 zenon_H1f3 zenon_H1f4. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_H96 | zenon_intro zenon_H5b ]. % 4.78/4.97 apply (zenon_L354_); trivial. % 4.78/4.97 apply (zenon_L109_); trivial. % 4.78/4.97 (* end of lemma zenon_L389_ *) % 4.78/4.97 assert (zenon_L390_ : ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (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) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e0) (e0)) = (e1)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((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)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e0) (e0)) = (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (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) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e1) (e1)) = (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e0) (e0)) = (e1)))) -> False). % 4.78/4.97 do 0 intro. intros zenon_H1e8 zenon_H122 zenon_H1b7 zenon_H172 zenon_H16f zenon_H16b zenon_H166 zenon_H86 zenon_H165 zenon_H170 zenon_H152 zenon_H114 zenon_H7b zenon_Hd0 zenon_H94 zenon_H137 zenon_Hac zenon_Ha0 zenon_H4c zenon_Ha4 zenon_Ha9 zenon_H9d zenon_Haf zenon_Hb3 zenon_Hb9 zenon_H11f zenon_H118 zenon_H13e zenon_H117 zenon_H70 zenon_H113 zenon_H153 zenon_H154 zenon_H171 zenon_H173 zenon_H174 zenon_H1b8 zenon_H1e zenon_H1f zenon_H100 zenon_Hfd zenon_H104 zenon_H33 zenon_H19d zenon_H37 zenon_H36 zenon_Hc3 zenon_H54 zenon_H1de zenon_H1e1 zenon_H13c zenon_H75 zenon_H142 zenon_H145 zenon_Hdf zenon_Hbe zenon_H132 zenon_H82 zenon_H76 zenon_H12e zenon_He9 zenon_H103 zenon_Hb4 zenon_H21 zenon_H1d zenon_H19c zenon_H35 zenon_He2 zenon_H6c zenon_H8f zenon_H41 zenon_H46 zenon_H4b zenon_H101 zenon_Hf9 zenon_Hf3 zenon_Hef zenon_Hf6 zenon_H102 zenon_Hd7 zenon_Hda zenon_Hdc zenon_He6 zenon_H110 zenon_H1c4 zenon_H1c3 zenon_H1c2 zenon_H1c0 zenon_H1b6 zenon_H19b zenon_H18f zenon_H194 zenon_H186 zenon_H198 zenon_H28 zenon_H175 zenon_H176 zenon_H177 zenon_H19a zenon_H1ba zenon_H1ab zenon_H1bb zenon_H1bf zenon_H1be zenon_H1c1 zenon_H1f2 zenon_H1ef zenon_H1f0 zenon_H1ee zenon_H1ec zenon_H1e9 zenon_H1ed zenon_H1ca zenon_H1c7 zenon_H1cb zenon_H1cc zenon_H11e zenon_H1c5 zenon_H1e2 zenon_H1bd zenon_H1e7 zenon_H1b9 zenon_H1f1 zenon_H1f3 zenon_H1f4 zenon_H89 zenon_H1f5. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H1f0); [ zenon_intro zenon_H135 | zenon_intro zenon_H38 ]. % 4.78/4.97 apply (zenon_L388_); trivial. % 4.78/4.97 apply (zenon_L384_); trivial. % 4.78/4.97 (* end of lemma zenon_L390_ *) % 4.78/4.97 assert (zenon_L391_ : ((~((op (e2) (e1)) = (e2)))\/(~((op (e0) (e0)) = (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((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 (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e0) (e0)) = (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((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)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (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 (e1) (e0)) = (e1))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e0) (e0)) = (e1)))) -> (~((op (e1) (e1)) = (e0))) -> False). % 4.78/4.97 do 0 intro. intros zenon_H1f5 zenon_H1d zenon_H21 zenon_Hb4 zenon_H94 zenon_H4c zenon_Hd0 zenon_H82 zenon_H89 zenon_H100 zenon_H1f zenon_H1e zenon_H19c zenon_H132 zenon_H137 zenon_H12e zenon_H11f zenon_H33 zenon_H37 zenon_H36 zenon_H35 zenon_H118 zenon_Hb9 zenon_Hac zenon_Ha0 zenon_Ha4 zenon_Ha9 zenon_H9d zenon_Haf zenon_Hb3 zenon_He2 zenon_H75 zenon_H76 zenon_H70 zenon_H6c zenon_H7b zenon_H8f zenon_H86 zenon_H117 zenon_H54 zenon_H41 zenon_H46 zenon_H4b zenon_H7c zenon_Hfd zenon_H103 zenon_H101 zenon_Hf9 zenon_Hf3 zenon_Hef zenon_Hf6 zenon_H102 zenon_Hbe zenon_Hdf zenon_Hd7 zenon_Hda zenon_Hdc zenon_He6 zenon_He9 zenon_H104 zenon_H110 zenon_H113 zenon_H114 zenon_H1c4 zenon_H1c3 zenon_H1b7 zenon_H1c2 zenon_H1c0 zenon_H1b6 zenon_H19b zenon_H18f zenon_H194 zenon_H186 zenon_H198 zenon_H28 zenon_H175 zenon_H176 zenon_H174 zenon_H173 zenon_H172 zenon_H16f zenon_H16b zenon_H166 zenon_H165 zenon_H170 zenon_H152 zenon_H13e zenon_H142 zenon_H13c zenon_H153 zenon_H154 zenon_H171 zenon_H177 zenon_H122 zenon_H19a zenon_H1ba zenon_H1ab zenon_H1bb zenon_H1bf zenon_H1be zenon_H1c1 zenon_H1f2 zenon_H1ef zenon_H1f0 zenon_H1ee zenon_H1ec zenon_H1e9 zenon_H1ed zenon_H1ca zenon_H1c7 zenon_H1cb zenon_H1cc zenon_H11e zenon_H1c5 zenon_H1de zenon_H1e1 zenon_H1e2 zenon_H1bd zenon_H1e7 zenon_H19d zenon_H1e8 zenon_H1b9 zenon_H1f1 zenon_H1f3 zenon_H1f4 zenon_H1b8 zenon_Hc3. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H1f0); [ zenon_intro zenon_H135 | zenon_intro zenon_H38 ]. % 4.78/4.97 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H95 | zenon_intro zenon_H145 ]. % 4.78/4.97 apply (zenon_L389_); trivial. % 4.78/4.97 apply (zenon_L390_); trivial. % 4.78/4.97 apply (zenon_L386_); trivial. % 4.78/4.97 (* end of lemma zenon_L391_ *) % 4.78/4.97 assert (zenon_L392_ : ((~((op (e2) (e1)) = (e2)))\/(~((op (e0) (e0)) = (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((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 (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e0) (e0)) = (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((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)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (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 (e1) (e0)) = (e1))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e0) (e0)) = (e1)))) -> False). % 4.83/4.98 do 0 intro. intros zenon_H1f5 zenon_H1d zenon_H21 zenon_Hb4 zenon_H94 zenon_H4c zenon_Hd0 zenon_H82 zenon_H89 zenon_H100 zenon_H1f zenon_H1e zenon_H19c zenon_H132 zenon_H137 zenon_H12e zenon_H11f zenon_H33 zenon_H37 zenon_H36 zenon_H35 zenon_H118 zenon_Hb9 zenon_Hac zenon_Ha0 zenon_Ha4 zenon_Ha9 zenon_H9d zenon_Haf zenon_Hb3 zenon_He2 zenon_H75 zenon_H76 zenon_H70 zenon_H6c zenon_H7b zenon_H8f zenon_H86 zenon_H117 zenon_H54 zenon_H41 zenon_H46 zenon_H4b zenon_H7c zenon_Hfd zenon_H103 zenon_H101 zenon_Hf9 zenon_Hf3 zenon_Hef zenon_Hf6 zenon_H102 zenon_Hbe zenon_Hdf zenon_Hd7 zenon_Hda zenon_Hdc zenon_He6 zenon_He9 zenon_H104 zenon_H110 zenon_H113 zenon_H114 zenon_H1c4 zenon_H1c3 zenon_H1b7 zenon_H1c2 zenon_H1c0 zenon_H1b6 zenon_H19b zenon_H18f zenon_H194 zenon_H186 zenon_H198 zenon_H28 zenon_H175 zenon_H176 zenon_H174 zenon_H173 zenon_H172 zenon_H16f zenon_H16b zenon_H166 zenon_H165 zenon_H170 zenon_H152 zenon_H13e zenon_H142 zenon_H13c zenon_H153 zenon_H154 zenon_H171 zenon_H177 zenon_H122 zenon_H19a zenon_H1ba zenon_H1ab zenon_H1bb zenon_H1bf zenon_H1be zenon_H1c1 zenon_H1f2 zenon_H1ef zenon_H1f0 zenon_H1ee zenon_H1ec zenon_H1e9 zenon_H1ed zenon_H1ca zenon_H1c7 zenon_H1cb zenon_H1cc zenon_H11e zenon_H1c5 zenon_H1de zenon_H1e1 zenon_H1e2 zenon_H1bd zenon_H1e7 zenon_H19d zenon_H1e8 zenon_H1b9 zenon_H1f1 zenon_H1f3 zenon_H1f4 zenon_H1b8. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H1f0); [ zenon_intro zenon_H135 | zenon_intro zenon_H38 ]. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H95 | zenon_intro zenon_Hc3 ]. % 4.83/4.98 apply (zenon_L389_); trivial. % 4.83/4.98 apply (zenon_L391_); trivial. % 4.83/4.98 apply (zenon_L386_); trivial. % 4.83/4.98 (* end of lemma zenon_L392_ *) % 4.83/4.98 assert (zenon_L393_ : ((~((op (e2) (e1)) = (e2)))\/(~((op (e0) (e0)) = (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((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 (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e0) (e0)) = (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((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)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e0) (e0)) = (e1)))) -> False). % 4.83/4.98 do 0 intro. intros zenon_H1f5 zenon_H1d zenon_H21 zenon_Hb4 zenon_H94 zenon_H4c zenon_Hd0 zenon_H82 zenon_H89 zenon_H100 zenon_H1f zenon_H1e zenon_H19c zenon_H132 zenon_H137 zenon_H12e zenon_H11f zenon_H33 zenon_H37 zenon_H35 zenon_H118 zenon_Hb9 zenon_Hac zenon_Ha0 zenon_Ha4 zenon_Ha9 zenon_H9d zenon_Haf zenon_Hb3 zenon_He2 zenon_H75 zenon_H76 zenon_H70 zenon_H6c zenon_H7b zenon_H8f zenon_H86 zenon_H117 zenon_H54 zenon_H41 zenon_H46 zenon_H4b zenon_Hfd zenon_H103 zenon_H101 zenon_Hf9 zenon_Hf3 zenon_Hef zenon_Hf6 zenon_H102 zenon_Hbe zenon_Hdf zenon_Hd7 zenon_Hda zenon_Hdc zenon_He6 zenon_He9 zenon_H104 zenon_H110 zenon_H113 zenon_H114 zenon_H1c4 zenon_H1c3 zenon_H1b7 zenon_H1c2 zenon_H1c0 zenon_H1b6 zenon_H19b zenon_H18f zenon_H194 zenon_H186 zenon_H198 zenon_H28 zenon_H175 zenon_H176 zenon_H174 zenon_H173 zenon_H172 zenon_H16f zenon_H16b zenon_H166 zenon_H165 zenon_H170 zenon_H152 zenon_H13e zenon_H142 zenon_H13c zenon_H153 zenon_H154 zenon_H171 zenon_H177 zenon_H122 zenon_H19a zenon_H1ba zenon_H1ab zenon_H1bb zenon_H1bf zenon_H1be zenon_H1c1 zenon_H1f2 zenon_H1ef zenon_H1f0 zenon_H1ee zenon_H1ec zenon_H1e9 zenon_H1ed zenon_H1ca zenon_H1c7 zenon_H1cb zenon_H1cc zenon_H11e zenon_H1c5 zenon_H1de zenon_H1e1 zenon_H1e2 zenon_H1bd zenon_H1e7 zenon_H19d zenon_H1e8 zenon_H1b9 zenon_H1f1 zenon_H1f3 zenon_H1f4 zenon_H1b8. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H7c | zenon_intro zenon_Hc3 ]. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H1b8); [ zenon_intro zenon_H36 | zenon_intro zenon_H5b ]. % 4.83/4.98 apply (zenon_L392_); trivial. % 4.83/4.98 apply (zenon_L206_); trivial. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H7c | zenon_intro zenon_H145 ]. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H1b8); [ zenon_intro zenon_H36 | zenon_intro zenon_H5b ]. % 4.83/4.98 apply (zenon_L391_); trivial. % 4.83/4.98 apply (zenon_L206_); trivial. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H1b8); [ zenon_intro zenon_H36 | zenon_intro zenon_H5b ]. % 4.83/4.98 apply (zenon_L390_); trivial. % 4.83/4.98 apply (zenon_L135_); trivial. % 4.83/4.98 (* end of lemma zenon_L393_ *) % 4.83/4.98 assert (zenon_L394_ : ((~((op (e1) (e1)) = (e1)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (~((e1) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (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) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (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 (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e0) (e0)) = (e1)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e0) (e0)) = (e1)))) -> False). % 4.83/4.98 do 0 intro. intros zenon_H1b8 zenon_H1f4 zenon_H1f3 zenon_H1f1 zenon_H1b9 zenon_H1e8 zenon_H19d zenon_H1e7 zenon_H1bd zenon_H1e2 zenon_H1e1 zenon_H1de zenon_H1c5 zenon_H11e zenon_H1cc zenon_H1cb zenon_H1c7 zenon_H1ca zenon_H1ed zenon_H1e9 zenon_H1ec zenon_H1ee zenon_H1f0 zenon_H1ef zenon_H1f2 zenon_H1c1 zenon_H1be zenon_H1bf zenon_H1bb zenon_H1ab zenon_H1ba zenon_H19a zenon_H122 zenon_H177 zenon_H171 zenon_H154 zenon_H153 zenon_H13c zenon_H142 zenon_H13e zenon_H152 zenon_H170 zenon_H165 zenon_H166 zenon_H16b zenon_H16f zenon_H172 zenon_H173 zenon_H174 zenon_H176 zenon_H175 zenon_H28 zenon_H198 zenon_H186 zenon_H194 zenon_H18f zenon_H19b zenon_H1b6 zenon_H1c0 zenon_H1c2 zenon_H1b7 zenon_H1c3 zenon_H1c4 zenon_H114 zenon_H113 zenon_H110 zenon_H104 zenon_He9 zenon_He6 zenon_Hdc zenon_Hda zenon_Hd7 zenon_Hdf zenon_Hbe zenon_H102 zenon_Hf6 zenon_Hef zenon_Hf3 zenon_Hf9 zenon_H101 zenon_H103 zenon_Hfd zenon_H4b zenon_H46 zenon_H41 zenon_H54 zenon_H117 zenon_H86 zenon_H8f zenon_H7b zenon_H6c zenon_H70 zenon_H76 zenon_H75 zenon_He2 zenon_Hb3 zenon_Haf zenon_H9d zenon_Ha9 zenon_Ha4 zenon_Ha0 zenon_Hac zenon_Hb9 zenon_H118 zenon_H35 zenon_H37 zenon_H33 zenon_H11f zenon_H12e zenon_H137 zenon_H132 zenon_H19c zenon_H1e zenon_H1f zenon_H100 zenon_H89 zenon_H82 zenon_Hd0 zenon_H4c zenon_H94 zenon_Hb4 zenon_H1d zenon_H1f5. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H1c1); [ zenon_intro zenon_H21 | zenon_intro zenon_H38 ]. % 4.83/4.98 apply (zenon_L393_); trivial. % 4.83/4.98 apply (zenon_L387_); trivial. % 4.83/4.98 (* end of lemma zenon_L394_ *) % 4.83/4.98 assert (zenon_L395_ : (((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) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (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) (e1)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (e1))) -> (~((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))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e0) (e0)) = (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e0) (e0)) = (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> False). % 4.83/4.98 do 0 intro. intros zenon_H1d zenon_H100 zenon_Hac zenon_H19d zenon_H16b zenon_H6c zenon_Hd0 zenon_H9d zenon_H1ff zenon_Hf9 zenon_H202 zenon_H1fb zenon_H94 zenon_H205 zenon_Hb3 zenon_Hb9 zenon_H36 zenon_H1de zenon_H1e1 zenon_H21 zenon_Hdf zenon_H145 zenon_H142 zenon_H75 zenon_H135 zenon_H179 zenon_H46 zenon_H4c zenon_H4b zenon_H117 zenon_Hbe zenon_Hc3 zenon_H132 zenon_H33 zenon_H82 zenon_H76 zenon_H12e zenon_H37 zenon_He9 zenon_H7b zenon_Hb4 zenon_H1ab zenon_H114 zenon_H1f zenon_H1e zenon_H1f5 zenon_H89 zenon_H1f4 zenon_H1f3 zenon_H1f1 zenon_H1b9 zenon_H1e7 zenon_H1bd zenon_H1e2 zenon_H1c5 zenon_H11e zenon_H1cc zenon_H1cb zenon_H1c7 zenon_H1ca zenon_H1ed zenon_H1e9 zenon_H1ec zenon_H1ee zenon_H1f0 zenon_H1ef zenon_H1f2 zenon_H1c1 zenon_H1be zenon_H1bf zenon_H1bb zenon_H1ba zenon_H19a zenon_H177 zenon_H176 zenon_H175 zenon_H28 zenon_H198 zenon_H186 zenon_H194 zenon_H18f zenon_H19b zenon_H1b6 zenon_H1c0 zenon_H1c2 zenon_H1c3 zenon_H1c4 zenon_H110 zenon_He6 zenon_Hdc zenon_Hda zenon_Hd7 zenon_H102 zenon_Hf6 zenon_Hef zenon_Hf3 zenon_H101 zenon_H41 zenon_H8f zenon_He2 zenon_H35 zenon_H19c zenon_H103 zenon_H13c zenon_H54 zenon_Hfd zenon_H1b8 zenon_H174 zenon_H173 zenon_H171 zenon_H154 zenon_H153 zenon_H113 zenon_H70 zenon_H13e zenon_H118 zenon_H11f zenon_Haf zenon_Ha9 zenon_Ha4 zenon_Ha0 zenon_H137 zenon_H152 zenon_H170 zenon_H165 zenon_H86 zenon_H166 zenon_H16f zenon_H172 zenon_H1b7 zenon_H122 zenon_H1e8. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_H96 | zenon_intro zenon_H5b ]. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H85 | zenon_intro zenon_H104 ]. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H2a | zenon_intro zenon_H5b ]. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H2c | zenon_intro zenon_H104 ]. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ]. % 4.83/4.98 exact (zenon_H1e zenon_H23). % 4.83/4.98 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ]. % 4.83/4.98 exact (zenon_H1f zenon_H25). % 4.83/4.98 apply (zenon_or_s _ _ zenon_H24); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H114); [ zenon_intro zenon_H23 | zenon_intro zenon_H115 ]. % 4.83/4.98 exact (zenon_H1e zenon_H23). % 4.83/4.98 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H34 | zenon_intro zenon_H116 ]. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hb6 | zenon_intro zenon_H105 ]. % 4.83/4.98 exact (zenon_Hb4 zenon_Hb6). % 4.83/4.98 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H5e | zenon_intro zenon_H106 ]. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H7b); [ zenon_intro zenon_H7e | zenon_intro zenon_H7d ]. % 4.83/4.98 apply (zenon_L110_); trivial. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H7d); [ zenon_intro zenon_H3e | zenon_intro zenon_H7f ]. % 4.83/4.98 exact (zenon_H36 zenon_H3e). % 4.83/4.98 apply (zenon_or_s _ _ zenon_H7f); [ zenon_intro zenon_H47 | zenon_intro zenon_H71 ]. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H1de); [ zenon_intro zenon_Hbd | zenon_intro zenon_H1df ]. % 4.83/4.98 apply (zenon_L359_); trivial. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_H10e | zenon_intro zenon_H1e0 ]. % 4.83/4.98 apply (zenon_L365_); trivial. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H6d ]. % 4.83/4.98 apply (zenon_L366_); trivial. % 4.83/4.98 exact (zenon_H145 zenon_H6d). % 4.83/4.98 exact (zenon_H135 zenon_H71). % 4.83/4.98 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_H92 | zenon_intro zenon_H8a ]. % 4.83/4.98 apply (zenon_L23_); trivial. % 4.83/4.98 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hb5 ]. % 4.83/4.98 exact (zenon_Hb4 zenon_Hb6). % 4.83/4.98 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hb7 ]. % 4.83/4.98 apply (zenon_L52_); trivial. % 4.83/4.98 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H98 | zenon_intro zenon_Hb0 ]. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H1de); [ zenon_intro zenon_Hbd | zenon_intro zenon_H1df ]. % 4.83/4.98 apply (zenon_L36_); trivial. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_H10e | zenon_intro zenon_H1e0 ]. % 4.83/4.98 apply (zenon_L379_); trivial. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H6d ]. % 4.83/4.98 apply (zenon_L366_); trivial. % 4.83/4.98 exact (zenon_H145 zenon_H6d). % 4.83/4.98 apply (zenon_L380_); trivial. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H42 | zenon_intro zenon_Hbd ]. % 4.83/4.98 apply (zenon_L381_); trivial. % 4.83/4.98 apply (zenon_L359_); trivial. % 4.83/4.98 exact (zenon_H21 zenon_H26). % 4.83/4.98 apply (zenon_L388_); trivial. % 4.83/4.98 apply (zenon_L135_); trivial. % 4.83/4.98 apply (zenon_L394_); trivial. % 4.83/4.98 apply (zenon_L132_); trivial. % 4.83/4.98 (* end of lemma zenon_L395_ *) % 4.83/4.98 assert (zenon_L396_ : ((~((op (e2) (e1)) = (e2)))\/(~((op (e0) (e0)) = (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((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 (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (~((e1) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (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) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (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 (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e0) (e0)) = (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e0) (e0)) = (e1)))) -> False). % 4.83/4.98 do 0 intro. intros zenon_H1f5 zenon_H1d zenon_H21 zenon_Hb4 zenon_H94 zenon_H4c zenon_Hd0 zenon_H82 zenon_H89 zenon_H100 zenon_H1f zenon_H1e zenon_H1f4 zenon_H1f3 zenon_H1f1 zenon_H1b9 zenon_H1e8 zenon_H19d zenon_H1e7 zenon_H1bd zenon_H1e2 zenon_H1e1 zenon_H1de zenon_H1c5 zenon_H11e zenon_H1cc zenon_H1cb zenon_H1c7 zenon_H1ca zenon_H1ed zenon_H1e9 zenon_H1ec zenon_H1ee zenon_H1f0 zenon_H1ef zenon_H1f2 zenon_H1c1 zenon_H1be zenon_H1bf zenon_H1bb zenon_H1ab zenon_H1ba zenon_H19a zenon_H122 zenon_H177 zenon_H171 zenon_H154 zenon_H153 zenon_H13c zenon_H142 zenon_H13e zenon_H152 zenon_H170 zenon_H165 zenon_H166 zenon_H16b zenon_H16f zenon_H172 zenon_H173 zenon_H174 zenon_H176 zenon_H175 zenon_H28 zenon_H198 zenon_H186 zenon_H194 zenon_H18f zenon_H19b zenon_H1b6 zenon_H1c0 zenon_H1c2 zenon_H1b7 zenon_H1c3 zenon_H1c4 zenon_H114 zenon_H113 zenon_H110 zenon_He9 zenon_He6 zenon_Hdc zenon_Hda zenon_Hd7 zenon_Hdf zenon_Hbe zenon_H102 zenon_Hf6 zenon_Hef zenon_Hf3 zenon_Hf9 zenon_H101 zenon_H103 zenon_Hfd zenon_H7c zenon_H4b zenon_H46 zenon_H41 zenon_H54 zenon_H117 zenon_H86 zenon_H8f zenon_H7b zenon_H6c zenon_H70 zenon_H76 zenon_H75 zenon_He2 zenon_Hb3 zenon_Haf zenon_H9d zenon_Ha9 zenon_Ha4 zenon_Ha0 zenon_Hac zenon_Hb9 zenon_H118 zenon_H35 zenon_H36 zenon_H37 zenon_H33 zenon_H11f zenon_H12e zenon_H137 zenon_H132 zenon_H19c zenon_H1ff zenon_H202 zenon_H1fb zenon_H205 zenon_H179 zenon_Hc3 zenon_H1b8. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H135 | zenon_intro zenon_H104 ]. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H95 | zenon_intro zenon_H145 ]. % 4.83/4.98 apply (zenon_L355_); trivial. % 4.83/4.98 apply (zenon_L395_); trivial. % 4.83/4.98 apply (zenon_L391_); trivial. % 4.83/4.98 (* end of lemma zenon_L396_ *) % 4.83/4.98 assert (zenon_L397_ : ((~((op (e2) (e1)) = (e2)))\/(~((op (e0) (e0)) = (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((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 (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (~((e1) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (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) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (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 (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e0) (e0)) = (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e0) (e0)) = (e1)))) -> False). % 4.83/4.98 do 0 intro. intros zenon_H1f5 zenon_H1d zenon_H21 zenon_Hb4 zenon_H94 zenon_H4c zenon_Hd0 zenon_H82 zenon_H89 zenon_H100 zenon_H1f zenon_H1e zenon_H1f4 zenon_H1f3 zenon_H1f1 zenon_H1b9 zenon_H1e8 zenon_H19d zenon_H1e7 zenon_H1bd zenon_H1e2 zenon_H1e1 zenon_H1de zenon_H1c5 zenon_H11e zenon_H1cc zenon_H1cb zenon_H1c7 zenon_H1ca zenon_H1ed zenon_H1e9 zenon_H1ec zenon_H1ee zenon_H1f0 zenon_H1ef zenon_H1f2 zenon_H1c1 zenon_H1be zenon_H1bf zenon_H1bb zenon_H1ab zenon_H1ba zenon_H19a zenon_H122 zenon_H177 zenon_H171 zenon_H154 zenon_H153 zenon_H13c zenon_H142 zenon_H13e zenon_H152 zenon_H170 zenon_H165 zenon_H166 zenon_H16b zenon_H16f zenon_H172 zenon_H173 zenon_H174 zenon_H176 zenon_H175 zenon_H28 zenon_H198 zenon_H186 zenon_H194 zenon_H18f zenon_H19b zenon_H1b6 zenon_H1c0 zenon_H1c2 zenon_H1b7 zenon_H1c3 zenon_H1c4 zenon_H114 zenon_H113 zenon_H110 zenon_He9 zenon_He6 zenon_Hdc zenon_Hda zenon_Hd7 zenon_Hdf zenon_Hbe zenon_H102 zenon_Hf6 zenon_Hef zenon_Hf3 zenon_Hf9 zenon_H101 zenon_H103 zenon_Hfd zenon_H7c zenon_H4b zenon_H46 zenon_H41 zenon_H54 zenon_H117 zenon_H86 zenon_H8f zenon_H7b zenon_H6c zenon_H70 zenon_H76 zenon_H75 zenon_He2 zenon_Hb3 zenon_Haf zenon_H9d zenon_Ha9 zenon_Ha4 zenon_Ha0 zenon_Hac zenon_Hb9 zenon_H118 zenon_H35 zenon_H36 zenon_H37 zenon_H33 zenon_H11f zenon_H12e zenon_H137 zenon_H132 zenon_H19c zenon_H1ff zenon_H202 zenon_H1fb zenon_H205 zenon_Hc3 zenon_H1b8. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H135 | zenon_intro zenon_H104 ]. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H95 | zenon_intro zenon_H179 ]. % 4.83/4.98 apply (zenon_L355_); trivial. % 4.83/4.98 apply (zenon_L396_); trivial. % 4.83/4.98 apply (zenon_L392_); trivial. % 4.83/4.98 (* end of lemma zenon_L397_ *) % 4.83/4.98 assert (zenon_L398_ : (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (~((e1) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (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 (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e1) (e1)) = (e1)))) -> False). % 4.83/4.98 do 0 intro. intros zenon_H205 zenon_H1fb zenon_H202 zenon_H1ff zenon_H1d zenon_H1f zenon_H1e zenon_H1bc zenon_H19c zenon_H19a zenon_H122 zenon_H11f zenon_H177 zenon_H171 zenon_H154 zenon_H153 zenon_H13c zenon_H142 zenon_H13e zenon_H12e zenon_H137 zenon_H132 zenon_H152 zenon_H170 zenon_H165 zenon_H166 zenon_H16b zenon_H16f zenon_H172 zenon_H173 zenon_H174 zenon_H176 zenon_H175 zenon_H198 zenon_H186 zenon_H194 zenon_H18f zenon_H19b zenon_H28 zenon_H33 zenon_H37 zenon_H35 zenon_H118 zenon_Hb9 zenon_Hac zenon_Ha0 zenon_Ha4 zenon_Ha9 zenon_H9d zenon_Haf zenon_Hb3 zenon_Hb4 zenon_He2 zenon_H75 zenon_H70 zenon_H6c zenon_H7b zenon_H82 zenon_H8f zenon_H89 zenon_H86 zenon_H117 zenon_H54 zenon_H94 zenon_H41 zenon_H46 zenon_H4b zenon_H100 zenon_Hfd zenon_H103 zenon_H101 zenon_Hf9 zenon_Hf3 zenon_Hef zenon_Hf6 zenon_H102 zenon_Hbe zenon_Hd0 zenon_Hdf zenon_Hd7 zenon_Hda zenon_Hdc zenon_He6 zenon_He9 zenon_H110 zenon_H113 zenon_H114 zenon_H11d zenon_H1b8 zenon_H1b7 zenon_H1bb zenon_H1b6 zenon_H1ba zenon_H1ab zenon_H1f5 zenon_H1c3 zenon_H1c2 zenon_H1c0 zenon_H1bf zenon_H1be zenon_H1c1 zenon_H1f2 zenon_H1ef zenon_H1f0 zenon_H1ee zenon_H1ec zenon_H1e9 zenon_H1ed zenon_H1ca zenon_H1c7 zenon_H1cb zenon_H1cc zenon_H11e zenon_H1c4 zenon_H1c5 zenon_H1de zenon_H1e1 zenon_H1e2 zenon_H1bd zenon_H1e7 zenon_H19d zenon_H1e8 zenon_H1b9 zenon_H1f1 zenon_H1f3 zenon_H1f4. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_H20 | zenon_intro zenon_H4c ]. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_H21 | zenon_intro zenon_H104 ]. % 4.83/4.98 apply (zenon_L1_); trivial. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H1c1); [ zenon_intro zenon_H21 | zenon_intro zenon_H38 ]. % 4.83/4.98 apply (zenon_L1_); trivial. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H1c2); [ zenon_intro zenon_H21 | zenon_intro zenon_H4d ]. % 4.83/4.98 apply (zenon_L1_); trivial. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H1be); [ zenon_intro zenon_H21 | zenon_intro zenon_H2c ]. % 4.83/4.98 apply (zenon_L1_); trivial. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H7c | zenon_intro zenon_Hc3 ]. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H1b8); [ zenon_intro zenon_H36 | zenon_intro zenon_H5b ]. % 4.83/4.98 apply (zenon_L349_); trivial. % 4.83/4.98 apply (zenon_L220_); trivial. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H1b8); [ zenon_intro zenon_H36 | zenon_intro zenon_H5b ]. % 4.83/4.98 apply (zenon_L189_); trivial. % 4.83/4.98 apply (zenon_L221_); trivial. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H20 | zenon_intro zenon_H76 ]. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_H21 | zenon_intro zenon_H104 ]. % 4.83/4.98 apply (zenon_L1_); trivial. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H1c1); [ zenon_intro zenon_H21 | zenon_intro zenon_H38 ]. % 4.83/4.98 apply (zenon_L1_); trivial. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H1c2); [ zenon_intro zenon_H21 | zenon_intro zenon_H4d ]. % 4.83/4.98 apply (zenon_L1_); trivial. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H1be); [ zenon_intro zenon_H21 | zenon_intro zenon_H2c ]. % 4.83/4.98 apply (zenon_L1_); trivial. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H7c | zenon_intro zenon_Hc3 ]. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H1b8); [ zenon_intro zenon_H36 | zenon_intro zenon_H5b ]. % 4.83/4.98 apply (zenon_L348_); trivial. % 4.83/4.98 apply (zenon_L220_); trivial. % 4.83/4.98 apply (zenon_L210_); trivial. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_H21 | zenon_intro zenon_H104 ]. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H7c | zenon_intro zenon_Hc3 ]. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H1b8); [ zenon_intro zenon_H36 | zenon_intro zenon_H5b ]. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H135 | zenon_intro zenon_H104 ]. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H95 | zenon_intro zenon_Hc3 ]. % 4.83/4.98 apply (zenon_L355_); trivial. % 4.83/4.98 apply (zenon_L397_); trivial. % 4.83/4.98 apply (zenon_L393_); trivial. % 4.83/4.98 apply (zenon_L207_); trivial. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H1c0); [ zenon_intro zenon_H7c | zenon_intro zenon_H179 ]. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H1b8); [ zenon_intro zenon_H36 | zenon_intro zenon_H5b ]. % 4.83/4.98 apply (zenon_L397_); trivial. % 4.83/4.98 apply (zenon_L206_); trivial. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H7c | zenon_intro zenon_H145 ]. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H1b8); [ zenon_intro zenon_H36 | zenon_intro zenon_H5b ]. % 4.83/4.98 apply (zenon_L396_); trivial. % 4.83/4.98 apply (zenon_L206_); trivial. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H1b8); [ zenon_intro zenon_H36 | zenon_intro zenon_H5b ]. % 4.83/4.98 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H135 | zenon_intro zenon_H104 ]. % 4.83/4.98 apply (zenon_L395_); trivial. % 4.83/4.98 apply (zenon_L390_); trivial. % 4.83/4.99 apply (zenon_L135_); trivial. % 4.83/4.99 apply (zenon_L394_); trivial. % 4.83/4.99 (* end of lemma zenon_L398_ *) % 4.83/4.99 assert (zenon_L399_ : ((~((op (e0) (e1)) = (e0)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e0) (e0)) = (e1)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e2))) -> (((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) (e1)) = (e3)))\/(~((op (e0) (e0)) = (e1)))) -> False). % 4.83/4.99 do 0 intro. intros zenon_H1f4 zenon_H1f3 zenon_H1f1 zenon_H1b9 zenon_H1e8 zenon_H1e7 zenon_H1bd zenon_H1e2 zenon_H1e1 zenon_H1de zenon_H1c5 zenon_H1c4 zenon_H1cc zenon_H1cb zenon_H1c7 zenon_H1ca zenon_H1ed zenon_H1e9 zenon_H1ec zenon_H1ee zenon_H1f0 zenon_H1ef zenon_H1f2 zenon_H1c1 zenon_H1be zenon_H1bf zenon_H1c0 zenon_H1c2 zenon_H1c3 zenon_H1f5 zenon_H1ba zenon_H1bb zenon_H11d zenon_H110 zenon_He6 zenon_Hf6 zenon_Hef zenon_Hf3 zenon_H101 zenon_H46 zenon_H89 zenon_H8f zenon_H6c zenon_H194 zenon_H186 zenon_H198 zenon_H1bc zenon_H1ff zenon_H202 zenon_H1fb zenon_H205 zenon_H11e zenon_H1b7 zenon_H19b zenon_H137 zenon_H13c zenon_H41 zenon_Hb9 zenon_H118 zenon_H18f zenon_H11f zenon_H1ab zenon_H165 zenon_H132 zenon_H166 zenon_H9d zenon_He9 zenon_H19a zenon_H175 zenon_H176 zenon_H174 zenon_H173 zenon_H172 zenon_H16f zenon_H16b zenon_Hbe zenon_H170 zenon_H152 zenon_H7b zenon_H94 zenon_Ha9 zenon_Haf zenon_H12e zenon_Hdf zenon_H13e zenon_H117 zenon_H142 zenon_H113 zenon_H153 zenon_H154 zenon_H171 zenon_H177 zenon_H122 zenon_H1b6 zenon_H1b8 zenon_H1e zenon_H1f zenon_H20 zenon_H114 zenon_Hb3 zenon_H28 zenon_Hac zenon_Hd0 zenon_H75 zenon_H2c zenon_Hf9 zenon_H86 zenon_H70 zenon_Hd7 zenon_Hda zenon_Hdc zenon_H145 zenon_He2 zenon_H96 zenon_H35 zenon_Hb4 zenon_H33 zenon_H38 zenon_H19d zenon_H36 zenon_Hc3 zenon_H103 zenon_H54 zenon_Hfd zenon_H4b zenon_H4d zenon_H179 zenon_H102 zenon_Ha4 zenon_Ha0 zenon_H1a7 zenon_H104 zenon_H82 zenon_H100 zenon_H1d zenon_H19c. % 4.83/4.99 apply (zenon_or_s _ _ zenon_H1bd); [ zenon_intro zenon_H4c | zenon_intro zenon_H37 ]. % 4.83/4.99 apply (zenon_L203_); trivial. % 4.83/4.99 apply (zenon_L398_); trivial. % 4.83/4.99 (* end of lemma zenon_L399_ *) % 4.83/4.99 assert (zenon_L400_ : ((~((op (e3) (e1)) = (e3)))\/(~((op (e0) (e0)) = (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((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 (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> False). % 4.83/4.99 do 0 intro. intros zenon_H19c zenon_H1d zenon_H118 zenon_H18f zenon_H13c zenon_Hb9 zenon_H41 zenon_H28 zenon_H2c zenon_H137 zenon_H9d zenon_H33 zenon_H38 zenon_H19d zenon_H36 zenon_Hc3 zenon_H103 zenon_H54 zenon_Hfd zenon_H4b zenon_H4d zenon_H179 zenon_H102 zenon_Ha4 zenon_Ha0 zenon_H1a7 zenon_H104 zenon_H82 zenon_H100 zenon_He9 zenon_H165 zenon_H132 zenon_H166 zenon_H195 zenon_Ha9 zenon_H7b zenon_H1ab zenon_Hb3 zenon_Hac zenon_Hd0 zenon_H75 zenon_Hf9 zenon_H86 zenon_H70 zenon_Hd7 zenon_Hda zenon_Hdc zenon_H145 zenon_He2 zenon_H35 zenon_H114 zenon_H20 zenon_H1f zenon_H1e zenon_H11e zenon_H1b7 zenon_H19b zenon_H11f zenon_H19a zenon_H175 zenon_H176 zenon_H174 zenon_H173 zenon_H172 zenon_H16f zenon_H16b zenon_Hbe zenon_H170 zenon_H152 zenon_H94 zenon_Haf zenon_H12e zenon_Hdf zenon_H13e zenon_H117 zenon_H142 zenon_H113 zenon_H153 zenon_H154 zenon_H171 zenon_H177 zenon_H122 zenon_H1b6 zenon_H1b8 zenon_H1f4 zenon_H1f3 zenon_H1f1 zenon_H1b9 zenon_H1e8 zenon_H1e7 zenon_H1bd zenon_H1e2 zenon_H1e1 zenon_H1de zenon_H1c5 zenon_H1c4 zenon_H1cc zenon_H1cb zenon_H1c7 zenon_H1ca zenon_H1ed zenon_H1e9 zenon_H1ec zenon_H1ee zenon_H1f0 zenon_H1ef zenon_H1f2 zenon_H1c1 zenon_H1be zenon_H1bf zenon_H1c0 zenon_H1c2 zenon_H1c3 zenon_H1f5 zenon_H1ba zenon_H1bb zenon_H11d zenon_H110 zenon_He6 zenon_Hf6 zenon_Hef zenon_Hf3 zenon_H101 zenon_H46 zenon_H89 zenon_H8f zenon_H6c zenon_H194 zenon_H186 zenon_H198 zenon_H1bc zenon_H1ff zenon_H202 zenon_H1fb zenon_H205. % 4.83/4.99 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_H96 | zenon_intro zenon_H5b ]. % 4.83/4.99 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H4c | zenon_intro zenon_Hb4 ]. % 4.83/4.99 apply (zenon_L199_); trivial. % 4.83/4.99 apply (zenon_L399_); trivial. % 4.83/4.99 apply (zenon_L343_); trivial. % 4.83/4.99 (* end of lemma zenon_L400_ *) % 4.83/4.99 assert (zenon_L401_ : (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (~((e1) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (e0))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e0) (e0)) = (e1)))) -> False). % 4.83/4.99 do 0 intro. intros zenon_H205 zenon_H1fb zenon_H202 zenon_H1ff zenon_H1c3 zenon_H1c2 zenon_H1c0 zenon_H1bf zenon_H1be zenon_H1c1 zenon_H1f2 zenon_H1ef zenon_H1f0 zenon_H1ee zenon_H1ec zenon_H1e9 zenon_H1ed zenon_H1ca zenon_H1c7 zenon_H1cb zenon_H1cc zenon_H1c4 zenon_H1c5 zenon_H1de zenon_H1e1 zenon_H1e2 zenon_H1e7 zenon_H1e8 zenon_H1f1 zenon_H1f3 zenon_H1f4 zenon_H1bb zenon_H1ba zenon_H1bc zenon_H1bd zenon_H19c zenon_H122 zenon_H11f zenon_H177 zenon_H171 zenon_H154 zenon_H153 zenon_H13c zenon_H142 zenon_H13e zenon_H12e zenon_H137 zenon_H132 zenon_H152 zenon_H170 zenon_H165 zenon_H166 zenon_H16b zenon_H16f zenon_H172 zenon_H173 zenon_H174 zenon_H176 zenon_H175 zenon_H198 zenon_H186 zenon_H194 zenon_H195 zenon_H18f zenon_H20 zenon_H19b zenon_H28 zenon_H2c zenon_H11e zenon_H1d zenon_H33 zenon_H38 zenon_H36 zenon_H35 zenon_H118 zenon_Hb9 zenon_Hac zenon_Ha0 zenon_Ha4 zenon_Ha9 zenon_H9d zenon_Haf zenon_Hb3 zenon_He2 zenon_H75 zenon_H70 zenon_H6c zenon_H7b zenon_H82 zenon_H8f zenon_H89 zenon_H86 zenon_H117 zenon_H54 zenon_H94 zenon_H41 zenon_H46 zenon_H4d zenon_H4b zenon_H7c zenon_H100 zenon_Hfd zenon_H103 zenon_H101 zenon_Hf9 zenon_Hf3 zenon_Hef zenon_Hf6 zenon_H102 zenon_Hbe zenon_Hd0 zenon_Hdf zenon_Hd7 zenon_Hda zenon_Hdc zenon_He6 zenon_He9 zenon_H104 zenon_H110 zenon_H113 zenon_H114 zenon_H1f zenon_H1e zenon_H11d zenon_H19a zenon_H19d zenon_Hc3 zenon_H179 zenon_H1a7 zenon_H1ab zenon_H1b7 zenon_H1b6 zenon_H1b8 zenon_H1b9 zenon_H1f5. % 4.83/4.99 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H95 | zenon_intro zenon_H145 ]. % 4.83/4.99 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_H96 | zenon_intro zenon_H5b ]. % 4.83/4.99 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H4c | zenon_intro zenon_Hb4 ]. % 4.83/4.99 apply (zenon_L200_); trivial. % 4.83/4.99 apply (zenon_L213_); trivial. % 4.83/4.99 apply (zenon_L195_); trivial. % 4.83/4.99 apply (zenon_L400_); trivial. % 4.83/4.99 (* end of lemma zenon_L401_ *) % 4.83/4.99 assert (zenon_L402_ : ((~((op (e0) (e1)) = (e0)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (~((e1) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (e0))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e0) (e0)) = (e1)))) -> False). % 4.83/4.99 do 0 intro. intros zenon_H1f4 zenon_H1f3 zenon_H1f1 zenon_H1e8 zenon_H1e7 zenon_H1e2 zenon_H1e1 zenon_H1de zenon_H1c5 zenon_H1c4 zenon_H1cc zenon_H1cb zenon_H1c7 zenon_H1ca zenon_H1ed zenon_H1e9 zenon_H1ec zenon_H1ee zenon_H1f0 zenon_H1ef zenon_H1f2 zenon_H1c1 zenon_H1be zenon_H1bf zenon_H1c0 zenon_H1c2 zenon_H1c3 zenon_H1ff zenon_H202 zenon_H1fb zenon_H205 zenon_H1bc zenon_H1bb zenon_H1bd zenon_H19c zenon_H122 zenon_H11f zenon_H177 zenon_H171 zenon_H154 zenon_H153 zenon_H13c zenon_H142 zenon_H13e zenon_H12e zenon_H137 zenon_H132 zenon_H152 zenon_H170 zenon_H165 zenon_H166 zenon_H16b zenon_H16f zenon_H172 zenon_H173 zenon_H174 zenon_H176 zenon_H175 zenon_H198 zenon_H186 zenon_H194 zenon_H195 zenon_H18f zenon_H20 zenon_H19b zenon_H28 zenon_H2c zenon_H11e zenon_H1d zenon_H33 zenon_H38 zenon_H36 zenon_H35 zenon_H118 zenon_Hb9 zenon_Hac zenon_Ha0 zenon_Ha4 zenon_Ha9 zenon_H9d zenon_Haf zenon_Hb3 zenon_He2 zenon_H75 zenon_H70 zenon_H6c zenon_H7b zenon_H82 zenon_H8f zenon_H89 zenon_H86 zenon_H117 zenon_H54 zenon_H94 zenon_H41 zenon_H46 zenon_H4d zenon_H4b zenon_H7c zenon_H100 zenon_Hfd zenon_H103 zenon_H101 zenon_Hf9 zenon_Hf3 zenon_Hef zenon_Hf6 zenon_H102 zenon_Hbe zenon_Hd0 zenon_Hdf zenon_Hd7 zenon_Hda zenon_Hdc zenon_He6 zenon_He9 zenon_H104 zenon_H110 zenon_H113 zenon_H114 zenon_H1f zenon_H1e zenon_H11d zenon_H19a zenon_H1b9 zenon_H1b8 zenon_H1b6 zenon_H1b7 zenon_H1ab zenon_H1a7 zenon_Hc3 zenon_H19d zenon_H1ba zenon_H1f5. % 4.83/4.99 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H95 | zenon_intro zenon_H179 ]. % 4.83/4.99 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_H96 | zenon_intro zenon_H5b ]. % 4.83/4.99 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H4c | zenon_intro zenon_Hb4 ]. % 4.83/4.99 apply (zenon_L201_); trivial. % 4.83/4.99 apply (zenon_L216_); trivial. % 4.83/4.99 apply (zenon_L217_); trivial. % 4.83/4.99 apply (zenon_L401_); trivial. % 4.83/4.99 (* end of lemma zenon_L402_ *) % 4.83/4.99 assert (zenon_L403_ : ((~((op (e3) (e1)) = (e3)))\/(~((op (e0) (e0)) = (e1)))) -> (((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))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e3) (e0)) = (op (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)))) -> (((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 (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e1) (e1)) = (e1)))) -> False). % 4.83/4.99 do 0 intro. intros zenon_H19c zenon_H1d zenon_H100 zenon_H82 zenon_H104 zenon_H1a7 zenon_Ha0 zenon_Ha4 zenon_H102 zenon_H179 zenon_H4d zenon_H4b zenon_Hfd zenon_H54 zenon_H103 zenon_Hc3 zenon_H36 zenon_H19d zenon_H38 zenon_H33 zenon_Hb4 zenon_H35 zenon_He2 zenon_H145 zenon_Hdc zenon_Hda zenon_Hd7 zenon_H70 zenon_H86 zenon_Hf9 zenon_H2c zenon_H75 zenon_Hd0 zenon_Hac zenon_H28 zenon_Hb3 zenon_H114 zenon_H20 zenon_H1f zenon_H1e zenon_H1b8 zenon_H1b6 zenon_H122 zenon_H177 zenon_H171 zenon_H154 zenon_H153 zenon_H113 zenon_H142 zenon_H117 zenon_H13e zenon_Hdf zenon_H12e zenon_Haf zenon_Ha9 zenon_H94 zenon_H7b zenon_H152 zenon_H170 zenon_Hbe zenon_H16b zenon_H16f zenon_H172 zenon_H173 zenon_H174 zenon_H176 zenon_H175 zenon_H19a zenon_He9 zenon_H9d zenon_H166 zenon_H132 zenon_H165 zenon_H1ab zenon_H11f zenon_H18f zenon_H118 zenon_Hb9 zenon_H41 zenon_H13c zenon_H137 zenon_H19b zenon_H1b7 zenon_H11e zenon_H205 zenon_H1fb zenon_H202 zenon_H1ff zenon_H1bc zenon_H198 zenon_H186 zenon_H194 zenon_H6c zenon_H8f zenon_H89 zenon_H46 zenon_H101 zenon_Hf3 zenon_Hef zenon_Hf6 zenon_He6 zenon_H110 zenon_H11d zenon_H1bb zenon_H1ba zenon_H1f5 zenon_H1c3 zenon_H1c2 zenon_H1c0 zenon_H1bf zenon_H1be zenon_H1c1 zenon_H1f2 zenon_H1ef zenon_H1f0 zenon_H1ee zenon_H1ec zenon_H1e9 zenon_H1ed zenon_H1ca zenon_H1c7 zenon_H1cb zenon_H1cc zenon_H1c4 zenon_H1c5 zenon_H1de zenon_H1e1 zenon_H1e2 zenon_H1bd zenon_H1e7 zenon_H1e8 zenon_H1b9 zenon_H1f1 zenon_H1f3 zenon_H1f4. % 4.83/4.99 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_H96 | zenon_intro zenon_H5b ]. % 4.83/4.99 apply (zenon_L399_); trivial. % 4.83/4.99 apply (zenon_L218_); trivial. % 4.83/4.99 (* end of lemma zenon_L403_ *) % 4.83/4.99 assert (zenon_L404_ : ((~((op (e0) (e1)) = (e0)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (~((e1) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (e0))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (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 (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e0) (e0)) = (e1)))) -> False). % 4.83/5.00 do 0 intro. intros zenon_H1f4 zenon_H1f3 zenon_H1f1 zenon_H1e8 zenon_H1e7 zenon_H1e2 zenon_H1e1 zenon_H1de zenon_H1c5 zenon_H1c4 zenon_H1cc zenon_H1cb zenon_H1c7 zenon_H1ca zenon_H1ed zenon_H1e9 zenon_H1ec zenon_H1ee zenon_H1f0 zenon_H1ef zenon_H1f2 zenon_H1c1 zenon_H1be zenon_H1bf zenon_H1c0 zenon_H1c2 zenon_H1c3 zenon_H1ba zenon_H1ff zenon_H202 zenon_H1fb zenon_H205 zenon_H1bd zenon_H1bb zenon_H1bc zenon_H19c zenon_H19a zenon_H122 zenon_H11f zenon_H177 zenon_H171 zenon_H154 zenon_H153 zenon_H13c zenon_H142 zenon_H13e zenon_H12e zenon_H137 zenon_H132 zenon_H152 zenon_H170 zenon_H165 zenon_H166 zenon_H16b zenon_H16f zenon_H172 zenon_H173 zenon_H174 zenon_H176 zenon_H175 zenon_H198 zenon_H186 zenon_H194 zenon_H195 zenon_H18f zenon_H20 zenon_H19b zenon_H28 zenon_H2c zenon_H11d zenon_H1e zenon_H1f zenon_H114 zenon_H113 zenon_H110 zenon_H104 zenon_He9 zenon_He6 zenon_Hdc zenon_Hda zenon_Hd7 zenon_Hdf zenon_Hd0 zenon_Hbe zenon_H102 zenon_Hf6 zenon_Hef zenon_Hf3 zenon_Hf9 zenon_H101 zenon_H103 zenon_Hfd zenon_H100 zenon_H7c zenon_H4b zenon_H4d zenon_H46 zenon_H41 zenon_H94 zenon_H54 zenon_H117 zenon_H86 zenon_H89 zenon_H8f zenon_H82 zenon_H7b zenon_H6c zenon_H70 zenon_H75 zenon_He2 zenon_Hb4 zenon_Hb3 zenon_Haf zenon_H9d zenon_Ha9 zenon_Ha4 zenon_Ha0 zenon_Hac zenon_Hb9 zenon_H118 zenon_H35 zenon_H36 zenon_H38 zenon_H33 zenon_H1d zenon_H11e zenon_H1a7 zenon_H179 zenon_Hc3 zenon_H19d zenon_H1b8 zenon_H1b6 zenon_H1ab zenon_H1b7 zenon_H1b9 zenon_H1f5. % 4.83/5.00 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H95 | zenon_intro zenon_H145 ]. % 4.83/5.00 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_H96 | zenon_intro zenon_H5b ]. % 4.83/5.00 apply (zenon_or_s _ _ zenon_H1bd); [ zenon_intro zenon_H4c | zenon_intro zenon_H37 ]. % 4.83/5.00 apply (zenon_L204_); trivial. % 4.83/5.00 apply (zenon_L212_); trivial. % 4.83/5.00 apply (zenon_L195_); trivial. % 4.83/5.00 apply (zenon_L403_); trivial. % 4.83/5.00 (* end of lemma zenon_L404_ *) % 4.83/5.00 assert (zenon_L405_ : (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> (~((e1) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (e0))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (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 (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e0) (e0)) = (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e0) (e0)) = (e1)))) -> False). % 4.83/5.00 do 0 intro. intros zenon_H205 zenon_H1fb zenon_H202 zenon_H1ff zenon_H1c3 zenon_H1c2 zenon_H1c0 zenon_H1bf zenon_H1be zenon_H1c1 zenon_H1f2 zenon_H1ef zenon_H1f0 zenon_H1ee zenon_H1ec zenon_H1e9 zenon_H1ed zenon_H1ca zenon_H1c7 zenon_H1cb zenon_H1cc zenon_H1c4 zenon_H1c5 zenon_H1de zenon_H1e1 zenon_H1e2 zenon_H1e7 zenon_H1e8 zenon_H1f1 zenon_H1f3 zenon_H1f4 zenon_H1bd zenon_H1bb zenon_H1bc zenon_H19c zenon_H19a zenon_H122 zenon_H11f zenon_H177 zenon_H171 zenon_H154 zenon_H153 zenon_H13c zenon_H142 zenon_H13e zenon_H12e zenon_H137 zenon_H132 zenon_H152 zenon_H170 zenon_H165 zenon_H166 zenon_H16b zenon_H16f zenon_H172 zenon_H173 zenon_H174 zenon_H176 zenon_H175 zenon_H198 zenon_H186 zenon_H194 zenon_H195 zenon_H18f zenon_H20 zenon_H19b zenon_H28 zenon_H2c zenon_H11d zenon_H1e zenon_H1f zenon_H114 zenon_H113 zenon_H110 zenon_H104 zenon_He9 zenon_He6 zenon_Hdc zenon_Hda zenon_Hd7 zenon_Hdf zenon_Hd0 zenon_Hbe zenon_H102 zenon_Hf6 zenon_Hef zenon_Hf3 zenon_Hf9 zenon_H101 zenon_H103 zenon_Hfd zenon_H100 zenon_H7c zenon_H4b zenon_H4d zenon_H46 zenon_H41 zenon_H94 zenon_H54 zenon_H117 zenon_H86 zenon_H89 zenon_H8f zenon_H82 zenon_H7b zenon_H6c zenon_H70 zenon_H75 zenon_He2 zenon_Hb4 zenon_Hb3 zenon_Haf zenon_H9d zenon_Ha9 zenon_Ha4 zenon_Ha0 zenon_Hac zenon_Hb9 zenon_H118 zenon_H35 zenon_H36 zenon_H38 zenon_H33 zenon_H1d zenon_H11e zenon_H1b9 zenon_H1b7 zenon_H1ab zenon_H1b6 zenon_H1b8 zenon_H19d zenon_Hc3 zenon_H1a7 zenon_H1ba zenon_H1f5. % 4.83/5.00 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H95 | zenon_intro zenon_H179 ]. % 4.83/5.00 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_H96 | zenon_intro zenon_H5b ]. % 4.83/5.00 apply (zenon_L216_); trivial. % 4.83/5.00 apply (zenon_L217_); trivial. % 4.83/5.00 apply (zenon_L404_); trivial. % 4.83/5.00 (* end of lemma zenon_L405_ *) % 4.83/5.00 assert (zenon_L406_ : ((~((op (e2) (e1)) = (e2)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e0) (e0)) = (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e1) (e1)) = (e1)))) -> False). % 4.83/5.00 do 0 intro. intros zenon_H1f5 zenon_H1bb zenon_H1b9 zenon_H1b7 zenon_H1ab zenon_H1b6 zenon_H1b8 zenon_H19d zenon_H1a7 zenon_H1ba zenon_H11e zenon_H1d zenon_H33 zenon_H38 zenon_H36 zenon_H35 zenon_H118 zenon_Hb9 zenon_Hac zenon_Ha0 zenon_Ha4 zenon_Ha9 zenon_H9d zenon_Haf zenon_Hb3 zenon_Hb4 zenon_He2 zenon_H75 zenon_H70 zenon_H6c zenon_H7b zenon_H82 zenon_H8f zenon_H89 zenon_H86 zenon_H117 zenon_H54 zenon_H94 zenon_H41 zenon_H46 zenon_H4d zenon_H4b zenon_H7c zenon_H100 zenon_Hfd zenon_H103 zenon_H101 zenon_Hf9 zenon_Hf3 zenon_Hef zenon_Hf6 zenon_H102 zenon_Hbe zenon_Hd0 zenon_Hdf zenon_Hd7 zenon_Hda zenon_Hdc zenon_He6 zenon_He9 zenon_H104 zenon_H110 zenon_H113 zenon_H114 zenon_H1f zenon_H1e zenon_H11d zenon_H2c zenon_H28 zenon_H19b zenon_H20 zenon_H18f zenon_H194 zenon_H186 zenon_H198 zenon_H175 zenon_H176 zenon_H174 zenon_H173 zenon_H172 zenon_H16f zenon_H16b zenon_H166 zenon_H165 zenon_H170 zenon_H152 zenon_H132 zenon_H137 zenon_H12e zenon_H13e zenon_H142 zenon_H13c zenon_H153 zenon_H154 zenon_H171 zenon_H177 zenon_H11f zenon_H122 zenon_H19a zenon_H19c zenon_H1bc zenon_H1bd zenon_H205 zenon_H1fb zenon_H202 zenon_H1ff zenon_H1c3 zenon_H1c2 zenon_H1c0 zenon_H1bf zenon_H1be zenon_H1c1 zenon_H1f2 zenon_H1ef zenon_H1f0 zenon_H1ee zenon_H1ec zenon_H1e9 zenon_H1ed zenon_H1ca zenon_H1c7 zenon_H1cb zenon_H1cc zenon_H1c4 zenon_H1c5 zenon_H1de zenon_H1e1 zenon_H1e2 zenon_H1e7 zenon_H1e8 zenon_H1f1 zenon_H1f3 zenon_H1f4. % 4.83/5.00 apply (zenon_or_s _ _ zenon_H1e7); [ zenon_intro zenon_H195 | zenon_intro zenon_H37 ]. % 4.83/5.00 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H95 | zenon_intro zenon_Hc3 ]. % 4.83/5.00 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_H96 | zenon_intro zenon_H5b ]. % 4.83/5.00 apply (zenon_L213_); trivial. % 4.83/5.00 apply (zenon_L215_); trivial. % 4.83/5.00 apply (zenon_L405_); trivial. % 4.83/5.00 apply (zenon_L349_); trivial. % 4.83/5.00 (* end of lemma zenon_L406_ *) % 4.83/5.00 assert (zenon_L407_ : ((~((op (e2) (e1)) = (e2)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e0) (e0)) = (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e1) (e1)) = (e1)))) -> False). % 4.83/5.00 do 0 intro. intros zenon_H1f5 zenon_H1b9 zenon_H1b7 zenon_H1ab zenon_H1b6 zenon_H1b8 zenon_H19d zenon_Hc3 zenon_H179 zenon_H1a7 zenon_H11e zenon_H1d zenon_H33 zenon_H38 zenon_H36 zenon_H35 zenon_H118 zenon_Hb9 zenon_Hac zenon_Ha0 zenon_Ha4 zenon_Ha9 zenon_H9d zenon_Haf zenon_Hb3 zenon_Hb4 zenon_He2 zenon_H75 zenon_H70 zenon_H6c zenon_H7b zenon_H82 zenon_H8f zenon_H89 zenon_H86 zenon_H117 zenon_H54 zenon_H94 zenon_H41 zenon_H46 zenon_H4d zenon_H4b zenon_H7c zenon_H100 zenon_Hfd zenon_H103 zenon_H101 zenon_Hf9 zenon_Hf3 zenon_Hef zenon_Hf6 zenon_H102 zenon_Hbe zenon_Hd0 zenon_Hdf zenon_Hd7 zenon_Hda zenon_Hdc zenon_He6 zenon_He9 zenon_H104 zenon_H110 zenon_H113 zenon_H114 zenon_H1f zenon_H1e zenon_H11d zenon_H2c zenon_H28 zenon_H19b zenon_H20 zenon_H18f zenon_H194 zenon_H186 zenon_H198 zenon_H175 zenon_H176 zenon_H174 zenon_H173 zenon_H172 zenon_H16f zenon_H16b zenon_H166 zenon_H165 zenon_H170 zenon_H152 zenon_H132 zenon_H137 zenon_H12e zenon_H13e zenon_H142 zenon_H13c zenon_H153 zenon_H154 zenon_H171 zenon_H177 zenon_H11f zenon_H122 zenon_H19a zenon_H19c zenon_H1bc zenon_H1bb zenon_H1bd zenon_H205 zenon_H1fb zenon_H202 zenon_H1ff zenon_H1ba zenon_H1c3 zenon_H1c2 zenon_H1c0 zenon_H1bf zenon_H1be zenon_H1c1 zenon_H1f2 zenon_H1ef zenon_H1f0 zenon_H1ee zenon_H1ec zenon_H1e9 zenon_H1ed zenon_H1ca zenon_H1c7 zenon_H1cb zenon_H1cc zenon_H1c4 zenon_H1c5 zenon_H1de zenon_H1e1 zenon_H1e2 zenon_H1e7 zenon_H1e8 zenon_H1f1 zenon_H1f3 zenon_H1f4. % 4.83/5.00 apply (zenon_or_s _ _ zenon_H1e7); [ zenon_intro zenon_H195 | zenon_intro zenon_H37 ]. % 4.83/5.00 apply (zenon_L404_); trivial. % 4.83/5.00 apply (zenon_L349_); trivial. % 4.83/5.00 (* end of lemma zenon_L407_ *) % 4.83/5.00 assert (zenon_L408_ : ((~((op (e0) (e1)) = (e0)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/(~((op (e1) (e1)) = (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e3) (e0)) = (e3)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e3) (e3)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((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 (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (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 (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e3) (e2)) = (e3)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e3) (e3)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e1) (e1)) = (e0)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e2) (e2)) = (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e3) (e3)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e0) (e0)) = (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e2) (e1)) = (e2)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e2) (e2)) = (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e0) (e0)) = (e3)))) -> ((~((op (e3) (e1)) = (e3)))\/(~((op (e0) (e0)) = (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e1) (e1)) = (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e1) (e1)) = (e1)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e3) (e3)) = (e1)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e1) (e1)) = (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e2) (e2)) = (e2)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e3) (e3)) = (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e0)) = (e2)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e2) (e2)) = (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e1) (e3)) = (e1)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e0) (e1)) = (e0)))\/(~((op (e2) (e2)) = (e1)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e1) (e1)) = (e3)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e2)) = (e1)))\/(~((op (e0) (e0)) = (e2)))) -> ((~((op (e1) (e0)) = (e1)))\/(~((op (e2) (e2)) = (e0)))) -> ((~((op (e0) (e3)) = (e0)))\/(~((op (e2) (e2)) = (e3)))) -> ((~((op (e0) (e2)) = (e0)))\/(~((op (e0) (e0)) = (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 4.83/5.00 do 0 intro. intros zenon_H208 zenon_H1f5 zenon_H1bb zenon_H1b9 zenon_H1b8 zenon_H1b6 zenon_H1b7 zenon_H1ab zenon_H1a7 zenon_H19d zenon_H1ba zenon_H19a zenon_H11d zenon_H114 zenon_H113 zenon_H110 zenon_He9 zenon_He6 zenon_Hdc zenon_Hda zenon_Hd7 zenon_Hdf zenon_Hd0 zenon_Hbe zenon_H102 zenon_Hf6 zenon_Hef zenon_Hf3 zenon_Hf9 zenon_H101 zenon_H103 zenon_Hfd zenon_H100 zenon_H4b zenon_H46 zenon_H41 zenon_H94 zenon_H54 zenon_H117 zenon_H86 zenon_H89 zenon_H8f zenon_H82 zenon_H7b zenon_H6c zenon_H70 zenon_H75 zenon_He2 zenon_Hb3 zenon_Haf zenon_H9d zenon_Ha9 zenon_Ha4 zenon_Ha0 zenon_Hac zenon_Hb9 zenon_H118 zenon_H35 zenon_H33 zenon_H11e zenon_H28 zenon_H19b zenon_H18f zenon_H194 zenon_H186 zenon_H198 zenon_H175 zenon_H176 zenon_H174 zenon_H173 zenon_H172 zenon_H16f zenon_H16b zenon_H166 zenon_H165 zenon_H170 zenon_H152 zenon_H132 zenon_H137 zenon_H12e zenon_H13e zenon_H142 zenon_H13c zenon_H153 zenon_H154 zenon_H171 zenon_H177 zenon_H11f zenon_H122 zenon_H19c zenon_H1bd zenon_H1bc zenon_H1f4 zenon_H1f3 zenon_H1f1 zenon_H1e8 zenon_H1e7 zenon_H1e2 zenon_H1e1 zenon_H1de zenon_H1c5 zenon_H1c4 zenon_H1cc zenon_H1cb zenon_H1c7 zenon_H1ca zenon_H1ed zenon_H1e9 zenon_H1ec zenon_H1ee zenon_H1f0 zenon_H1ef zenon_H1f2 zenon_H1c1 zenon_H1be zenon_H1bf zenon_H1c0 zenon_H1c2 zenon_H1c3 zenon_H1ff zenon_H202 zenon_H1fb zenon_H205 zenon_H1e zenon_H1d. % 4.83/5.00 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H1f | zenon_intro zenon_H5b ]. % 4.83/5.00 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H20 | zenon_intro zenon_Hb4 ]. % 4.83/5.00 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_H21 | zenon_intro zenon_H104 ]. % 4.83/5.00 apply (zenon_L1_); trivial. % 4.83/5.00 apply (zenon_or_s _ _ zenon_H1c1); [ zenon_intro zenon_H21 | zenon_intro zenon_H38 ]. % 4.83/5.00 apply (zenon_L1_); trivial. % 4.83/5.00 apply (zenon_or_s _ _ zenon_H1c2); [ zenon_intro zenon_H21 | zenon_intro zenon_H4d ]. % 4.83/5.00 apply (zenon_L1_); trivial. % 4.83/5.00 apply (zenon_or_s _ _ zenon_H1be); [ zenon_intro zenon_H21 | zenon_intro zenon_H2c ]. % 4.83/5.00 apply (zenon_L1_); trivial. % 4.83/5.00 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H7c | zenon_intro zenon_Hc3 ]. % 4.83/5.00 apply (zenon_or_s _ _ zenon_H1b8); [ zenon_intro zenon_H36 | zenon_intro zenon_H5b ]. % 4.83/5.00 apply (zenon_or_s _ _ zenon_H1bf); [ zenon_intro zenon_H195 | zenon_intro zenon_Hb4 ]. % 4.83/5.00 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H95 | zenon_intro zenon_Hc3 ]. % 4.83/5.00 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_H96 | zenon_intro zenon_H5b ]. % 4.83/5.00 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H4c | zenon_intro zenon_Hb4 ]. % 4.83/5.00 apply (zenon_or_s _ _ zenon_H1bb); [ zenon_intro zenon_H29 | zenon_intro zenon_Hc3 ]. % 4.83/5.00 apply (zenon_L162_); trivial. % 4.83/5.00 apply (zenon_L201_); trivial. % 4.83/5.00 apply (zenon_L213_); trivial. % 4.83/5.00 apply (zenon_L215_); trivial. % 4.83/5.00 apply (zenon_L402_); trivial. % 4.83/5.00 apply (zenon_L406_); trivial. % 4.83/5.00 apply (zenon_L220_); trivial. % 4.83/5.00 apply (zenon_or_s _ _ zenon_H1c0); [ zenon_intro zenon_H7c | zenon_intro zenon_H179 ]. % 4.83/5.00 apply (zenon_or_s _ _ zenon_H1b8); [ zenon_intro zenon_H36 | zenon_intro zenon_H5b ]. % 4.83/5.00 apply (zenon_or_s _ _ zenon_H1bf); [ zenon_intro zenon_H195 | zenon_intro zenon_Hb4 ]. % 4.83/5.00 apply (zenon_L402_); trivial. % 4.83/5.00 apply (zenon_L406_); trivial. % 4.83/5.00 apply (zenon_L220_); trivial. % 4.83/5.00 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H7c | zenon_intro zenon_H145 ]. % 4.83/5.00 apply (zenon_or_s _ _ zenon_H1b8); [ zenon_intro zenon_H36 | zenon_intro zenon_H5b ]. % 4.83/5.00 apply (zenon_or_s _ _ zenon_H1bf); [ zenon_intro zenon_H195 | zenon_intro zenon_Hb4 ]. % 4.83/5.00 apply (zenon_L401_); trivial. % 4.83/5.00 apply (zenon_L407_); trivial. % 4.83/5.00 apply (zenon_L223_); trivial. % 4.83/5.00 apply (zenon_or_s _ _ zenon_H1b8); [ zenon_intro zenon_H36 | zenon_intro zenon_H5b ]. % 4.83/5.00 apply (zenon_or_s _ _ zenon_H1bf); [ zenon_intro zenon_H195 | zenon_intro zenon_Hb4 ]. % 4.83/5.00 apply (zenon_L400_); trivial. % 4.83/5.00 apply (zenon_L403_); trivial. % 4.83/5.00 apply (zenon_L196_); trivial. % 4.83/5.00 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H20 | zenon_intro zenon_H37 ]. % 4.83/5.00 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_H21 | zenon_intro zenon_H104 ]. % 4.83/5.00 apply (zenon_L1_); trivial. % 4.83/5.00 apply (zenon_or_s _ _ zenon_H1c1); [ zenon_intro zenon_H21 | zenon_intro zenon_H38 ]. % 4.83/5.00 apply (zenon_L1_); trivial. % 4.83/5.00 apply (zenon_or_s _ _ zenon_H1c2); [ zenon_intro zenon_H21 | zenon_intro zenon_H4d ]. % 4.83/5.00 apply (zenon_L1_); trivial. % 4.83/5.00 apply (zenon_or_s _ _ zenon_H1be); [ zenon_intro zenon_H21 | zenon_intro zenon_H2c ]. % 4.83/5.00 apply (zenon_L1_); trivial. % 4.83/5.00 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H7c | zenon_intro zenon_Hc3 ]. % 4.83/5.00 apply (zenon_or_s _ _ zenon_H1b8); [ zenon_intro zenon_H36 | zenon_intro zenon_H5b ]. % 4.83/5.00 apply (zenon_L406_); trivial. % 4.83/5.00 apply (zenon_L220_); trivial. % 4.83/5.00 apply (zenon_or_s _ _ zenon_H1c0); [ zenon_intro zenon_H7c | zenon_intro zenon_H179 ]. % 4.83/5.00 apply (zenon_or_s _ _ zenon_H1b8); [ zenon_intro zenon_H36 | zenon_intro zenon_H5b ]. % 4.83/5.00 apply (zenon_or_s _ _ zenon_H1e7); [ zenon_intro zenon_H195 | zenon_intro zenon_H37 ]. % 4.83/5.00 apply (zenon_L405_); trivial. % 4.83/5.00 apply (zenon_L349_); trivial. % 4.83/5.00 apply (zenon_L220_); trivial. % 4.83/5.00 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H7c | zenon_intro zenon_H145 ]. % 4.83/5.00 apply (zenon_or_s _ _ zenon_H1b8); [ zenon_intro zenon_H36 | zenon_intro zenon_H5b ]. % 4.83/5.00 apply (zenon_L407_); trivial. % 4.83/5.00 apply (zenon_L222_); trivial. % 4.83/5.00 apply (zenon_or_s _ _ zenon_H1b8); [ zenon_intro zenon_H36 | zenon_intro zenon_H5b ]. % 4.83/5.00 apply (zenon_L403_); trivial. % 4.83/5.00 apply (zenon_L196_); trivial. % 4.83/5.00 apply (zenon_L398_); trivial. % 4.83/5.00 apply (zenon_L344_); trivial. % 4.83/5.00 (* end of lemma zenon_L408_ *) % 4.83/5.00 apply (zenon_and_s _ _ ax1). zenon_intro zenon_H11f. zenon_intro zenon_H209. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H209). zenon_intro zenon_H1ff. zenon_intro zenon_H20a. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H20a). zenon_intro zenon_H20c. zenon_intro zenon_H20b. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H20b). zenon_intro zenon_H8f. zenon_intro zenon_H20d. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H20d). zenon_intro zenon_H20f. zenon_intro zenon_H20e. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H20e). zenon_intro zenon_H33. zenon_intro zenon_H210. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H210). zenon_intro zenon_H212. zenon_intro zenon_H211. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H211). zenon_intro zenon_Hdc. zenon_intro zenon_H213. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H213). zenon_intro zenon_Hf3. zenon_intro zenon_H214. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H214). zenon_intro zenon_H216. zenon_intro zenon_H215. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H215). zenon_intro zenon_H4b. zenon_intro zenon_H217. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H217). zenon_intro zenon_H219. zenon_intro zenon_H218. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H218). zenon_intro zenon_H1e9. zenon_intro zenon_H21a. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H21a). zenon_intro zenon_H110. zenon_intro zenon_H21b. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H21b). zenon_intro zenon_H21c. zenon_intro zenon_H75. % 4.83/5.00 apply (zenon_and_s _ _ ax2). zenon_intro zenon_H1d. zenon_intro zenon_H21d. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H21d). zenon_intro zenon_H114. zenon_intro zenon_H21e. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H21e). zenon_intro zenon_H118. zenon_intro zenon_H21f. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H21f). zenon_intro zenon_H137. zenon_intro zenon_H220. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H220). zenon_intro zenon_H100. zenon_intro zenon_H221. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H221). zenon_intro zenon_Hb3. zenon_intro zenon_H222. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H222). zenon_intro zenon_H103. zenon_intro zenon_H223. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H223). zenon_intro zenon_H186. zenon_intro zenon_H224. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H224). zenon_intro zenon_He9. zenon_intro zenon_H225. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H225). zenon_intro zenon_H1a7. zenon_intro zenon_H226. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H226). zenon_intro zenon_H7b. zenon_intro zenon_H227. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H227). zenon_intro zenon_H101. zenon_intro zenon_H228. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H228). zenon_intro zenon_H165. zenon_intro zenon_H229. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H229). zenon_intro zenon_Hac. zenon_intro zenon_H22a. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H22a). zenon_intro zenon_H166. zenon_intro zenon_H22b. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H22b). zenon_intro zenon_H202. zenon_intro zenon_H22c. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H22c). zenon_intro zenon_H1c7. zenon_intro zenon_H22d. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H22d). zenon_intro zenon_H102. zenon_intro zenon_H22e. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H22e). zenon_intro zenon_H16b. zenon_intro zenon_H22f. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H22f). zenon_intro zenon_H194. zenon_intro zenon_H230. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H230). zenon_intro zenon_H94. zenon_intro zenon_H231. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H231). zenon_intro zenon_Ha9. zenon_intro zenon_H232. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H232). zenon_intro zenon_He2. zenon_intro zenon_H233. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H233). zenon_intro zenon_H18f. zenon_intro zenon_H234. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H234). zenon_intro zenon_H1de. zenon_intro zenon_H235. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H235). zenon_intro zenon_H117. zenon_intro zenon_H236. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H236). zenon_intro zenon_H1e2. zenon_intro zenon_H237. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H237). zenon_intro zenon_Hdf. zenon_intro zenon_H238. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H238). zenon_intro zenon_H23a. zenon_intro zenon_H239. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H239). zenon_intro zenon_H12e. zenon_intro zenon_H23b. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H23b). zenon_intro zenon_H28. zenon_intro zenon_H23c. % 4.83/5.00 apply (zenon_and_s _ _ ax3). zenon_intro zenon_H23e. zenon_intro zenon_H23d. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H23d). zenon_intro zenon_H240. zenon_intro zenon_H23f. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H23f). zenon_intro zenon_H242. zenon_intro zenon_H241. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H241). zenon_intro zenon_H1ab. zenon_intro zenon_H243. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H243). zenon_intro zenon_Hbe. zenon_intro zenon_H244. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H244). zenon_intro zenon_H205. zenon_intro zenon_H245. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H245). zenon_intro zenon_H19d. zenon_intro zenon_H246. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H246). zenon_intro zenon_Hd0. zenon_intro zenon_H247. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H247). zenon_intro zenon_H198. zenon_intro zenon_H248. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H248). zenon_intro zenon_H24a. zenon_intro zenon_H249. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H249). zenon_intro zenon_H24c. zenon_intro zenon_H24b. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H24b). zenon_intro zenon_H24e. zenon_intro zenon_H24d. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H24d). zenon_intro zenon_H132. zenon_intro zenon_H24f. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H24f). zenon_intro zenon_H251. zenon_intro zenon_H250. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H250). zenon_intro zenon_H1e1. zenon_intro zenon_H252. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H252). zenon_intro zenon_H46. zenon_intro zenon_H253. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H253). zenon_intro zenon_H255. zenon_intro zenon_H254. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H254). zenon_intro zenon_H257. zenon_intro zenon_H256. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H256). zenon_intro zenon_H86. zenon_intro zenon_H258. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H258). zenon_intro zenon_H89. zenon_intro zenon_H259. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H259). zenon_intro zenon_H6c. zenon_intro zenon_H25a. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H25a). zenon_intro zenon_Hda. zenon_intro zenon_H25b. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H25b). zenon_intro zenon_H70. zenon_intro zenon_H25c. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H25c). zenon_intro zenon_H142. zenon_intro zenon_H25d. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H25d). zenon_intro zenon_H25f. zenon_intro zenon_H25e. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H25e). zenon_intro zenon_H261. zenon_intro zenon_H260. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H260). zenon_intro zenon_H263. zenon_intro zenon_H262. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H262). zenon_intro zenon_H265. zenon_intro zenon_H264. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H264). zenon_intro zenon_H1fb. zenon_intro zenon_H266. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H266). zenon_intro zenon_H268. zenon_intro zenon_H267. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H267). zenon_intro zenon_H35. zenon_intro zenon_H269. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H269). zenon_intro zenon_Ha0. zenon_intro zenon_H26a. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H26a). zenon_intro zenon_Hd7. zenon_intro zenon_H26b. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H26b). zenon_intro zenon_He6. zenon_intro zenon_H26c. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H26c). zenon_intro zenon_H26e. zenon_intro zenon_H26d. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H26d). zenon_intro zenon_H270. zenon_intro zenon_H26f. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H26f). zenon_intro zenon_Hef. zenon_intro zenon_H271. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H271). zenon_intro zenon_H41. zenon_intro zenon_H272. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H272). zenon_intro zenon_H13e. zenon_intro zenon_H273. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H273). zenon_intro zenon_H275. zenon_intro zenon_H274. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H274). zenon_intro zenon_H277. zenon_intro zenon_H276. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H276). zenon_intro zenon_H279. zenon_intro zenon_H278. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H278). zenon_intro zenon_Haf. zenon_intro zenon_H27a. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H27a). zenon_intro zenon_Hf6. zenon_intro zenon_H27b. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H27b). zenon_intro zenon_H113. zenon_intro zenon_H27c. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H27c). zenon_intro zenon_Ha4. zenon_intro zenon_H27d. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H27d). zenon_intro zenon_Hf9. zenon_intro zenon_H27e. % 4.83/5.00 apply (zenon_and_s _ _ ax4). zenon_intro zenon_Hb9. zenon_intro zenon_H27f. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H27f). zenon_intro zenon_H82. zenon_intro zenon_H280. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H280). zenon_intro zenon_H54. zenon_intro zenon_H281. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H281). zenon_intro zenon_H9d. zenon_intro zenon_H282. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H282). zenon_intro zenon_H13c. zenon_intro zenon_Hfd. % 4.83/5.00 apply (zenon_and_s _ _ ax5). zenon_intro zenon_H284. zenon_intro zenon_H283. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H283). zenon_intro zenon_H286. zenon_intro zenon_H285. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H285). zenon_intro zenon_H288. zenon_intro zenon_H287. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H287). zenon_intro zenon_H28a. zenon_intro zenon_H289. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H289). zenon_intro zenon_H208. zenon_intro zenon_H28b. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H28b). zenon_intro zenon_H1f4. zenon_intro zenon_H28c. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H28c). zenon_intro zenon_H1f2. zenon_intro zenon_H28d. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H28d). zenon_intro zenon_H1f3. zenon_intro zenon_H28e. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H28e). zenon_intro zenon_H1c3. zenon_intro zenon_H28f. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H28f). zenon_intro zenon_H175. zenon_intro zenon_H290. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H290). zenon_intro zenon_H177. zenon_intro zenon_H291. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H291). zenon_intro zenon_H176. zenon_intro zenon_H292. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H292). zenon_intro zenon_H122. zenon_intro zenon_H293. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H293). zenon_intro zenon_H1c1. zenon_intro zenon_H294. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H294). zenon_intro zenon_H1c2. zenon_intro zenon_H295. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H295). zenon_intro zenon_H1be. zenon_intro zenon_H296. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H296). zenon_intro zenon_H298. zenon_intro zenon_H297. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H297). zenon_intro zenon_H174. zenon_intro zenon_H299. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H299). zenon_intro zenon_H1c0. zenon_intro zenon_H29a. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H29a). zenon_intro zenon_H173. zenon_intro zenon_H29b. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H29b). zenon_intro zenon_H1b8. zenon_intro zenon_H29c. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H29c). zenon_intro zenon_H1b7. zenon_intro zenon_H29d. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H29d). zenon_intro zenon_H29f. zenon_intro zenon_H29e. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H29e). zenon_intro zenon_H2a1. zenon_intro zenon_H2a0. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H2a0). zenon_intro zenon_H1bf. zenon_intro zenon_H2a2. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H2a2). zenon_intro zenon_H1e7. zenon_intro zenon_H2a3. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H2a3). zenon_intro zenon_H1cc. zenon_intro zenon_H2a4. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H2a4). zenon_intro zenon_H1cb. zenon_intro zenon_H2a5. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H2a5). zenon_intro zenon_H171. zenon_intro zenon_H2a6. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H2a6). zenon_intro zenon_H1f0. zenon_intro zenon_H2a7. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H2a7). zenon_intro zenon_H1ef. zenon_intro zenon_H2a8. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H2a8). zenon_intro zenon_H1f1. zenon_intro zenon_H2a9. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H2a9). zenon_intro zenon_H2ab. zenon_intro zenon_H2aa. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H2aa). zenon_intro zenon_H172. zenon_intro zenon_H2ac. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H2ac). zenon_intro zenon_H1ca. zenon_intro zenon_H2ad. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H2ad). zenon_intro zenon_H170. zenon_intro zenon_H2ae. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H2ae). zenon_intro zenon_H1f5. zenon_intro zenon_H2af. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H2af). zenon_intro zenon_H2b1. zenon_intro zenon_H2b0. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H2b0). zenon_intro zenon_H16f. zenon_intro zenon_H2b2. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H2b2). zenon_intro zenon_H154. zenon_intro zenon_H2b3. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H2b3). zenon_intro zenon_H1b6. zenon_intro zenon_H2b4. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H2b4). zenon_intro zenon_H1bd. zenon_intro zenon_H2b5. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H2b5). zenon_intro zenon_H1bc. zenon_intro zenon_H2b6. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H2b6). zenon_intro zenon_H2b8. zenon_intro zenon_H2b7. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H2b7). zenon_intro zenon_H152. zenon_intro zenon_H2b9. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H2b9). zenon_intro zenon_H1ee. zenon_intro zenon_H2ba. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H2ba). zenon_intro zenon_H1ed. zenon_intro zenon_H2bb. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H2bb). zenon_intro zenon_H1ec. zenon_intro zenon_H2bc. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H2bc). zenon_intro zenon_H2be. zenon_intro zenon_H2bd. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H2bd). zenon_intro zenon_H1bb. zenon_intro zenon_H2bf. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H2bf). zenon_intro zenon_H1ba. zenon_intro zenon_H2c0. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H2c0). zenon_intro zenon_H1b9. zenon_intro zenon_H2c1. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H2c1). zenon_intro zenon_H19c. zenon_intro zenon_H2c2. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H2c2). zenon_intro zenon_H2c4. zenon_intro zenon_H2c3. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H2c3). zenon_intro zenon_H19b. zenon_intro zenon_H2c5. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H2c5). zenon_intro zenon_H2c7. zenon_intro zenon_H2c6. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H2c6). zenon_intro zenon_H19a. zenon_intro zenon_H2c8. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H2c8). zenon_intro zenon_H11e. zenon_intro zenon_H2c9. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H2c9). zenon_intro zenon_H2cb. zenon_intro zenon_H2ca. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H2ca). zenon_intro zenon_H11d. zenon_intro zenon_H2cc. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H2cc). zenon_intro zenon_H153. zenon_intro zenon_H2cd. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H2cd). zenon_intro zenon_H1e8. zenon_intro zenon_H2ce. % 4.83/5.00 apply (zenon_and_s _ _ zenon_H2ce). zenon_intro zenon_H1c5. zenon_intro zenon_H1c4. % 4.83/5.00 apply (zenon_or_s _ _ zenon_H284); [ zenon_intro zenon_H1e | zenon_intro zenon_H1e ]. % 4.83/5.00 apply (zenon_L408_); trivial. % 4.83/5.00 apply (zenon_L408_); trivial. % 4.83/5.00 Qed. % 4.83/5.00 % SZS output end Proof % 4.83/5.00 (* END-PROOF *) % 4.83/5.00 nodes searched: 183408 % 4.83/5.00 max branch formulas: 386 % 4.83/5.00 proof nodes created: 5453 % 4.83/5.00 formulas created: 38901 % 4.83/5.00 %------------------------------------------------------------------------------