%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : ALG135+1 : TPTP v8.1.0. Released v2.7.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n026.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Thu Jul 14 18:30:08 EDT 2022 % Result : Unsatisfiable 3.86s 4.02s % Output : Proof 3.86s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : ALG135+1 : TPTP v8.1.0. Released v2.7.0. % 0.03/0.12 % Command : run_zenon %s %d % 0.12/0.32 % Computer : n026.cluster.edu % 0.12/0.32 % Model : x86_64 x86_64 % 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.32 % Memory : 8042.1875MB % 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.32 % CPULimit : 300 % 0.12/0.32 % WCLimit : 600 % 0.12/0.32 % DateTime : Wed Jun 8 15:14:47 EDT 2022 % 0.12/0.33 % CPUTime : % 3.86/4.02 (* PROOF-FOUND *) % 3.86/4.02 % SZS status Unsatisfiable % 3.86/4.02 (* BEGIN-PROOF *) % 3.86/4.02 % SZS output start Proof % 3.86/4.02 Theorem zenon_thm : False. % 3.86/4.02 Proof. % 3.86/4.02 assert (zenon_L1_ : (((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))) -> False). % 3.86/4.02 do 0 intro. intros zenon_H1d. % 3.86/4.02 apply (zenon_and_s _ _ zenon_H1d). zenon_intro zenon_H1f. zenon_intro zenon_H1e. % 3.86/4.02 exact (zenon_H1e zenon_H1f). % 3.86/4.02 (* end of lemma zenon_L1_ *) % 3.86/4.02 assert (zenon_L2_ : (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e3)) = (e0)) -> False). % 3.86/4.02 do 0 intro. intros zenon_H20 zenon_H21 zenon_H22. % 3.86/4.02 cut (((op (e0) (e2)) = (e0)) = ((op (e0) (e2)) = (op (e0) (e3)))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_H20. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H21. % 3.86/4.02 cut (((e0) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H23]. % 3.86/4.02 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H24]. % 3.86/4.02 congruence. % 3.86/4.02 apply zenon_H24. apply refl_equal. % 3.86/4.02 apply zenon_H23. apply sym_equal. exact zenon_H22. % 3.86/4.02 (* end of lemma zenon_L2_ *) % 3.86/4.02 assert (zenon_L3_ : (((op (e0) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> False). % 3.86/4.02 do 0 intro. intros zenon_H25 zenon_H21 zenon_H20. % 3.86/4.02 apply (zenon_and_s _ _ zenon_H25). zenon_intro zenon_H22. zenon_intro zenon_H26. % 3.86/4.02 apply (zenon_L2_); trivial. % 3.86/4.02 (* end of lemma zenon_L3_ *) % 3.86/4.02 assert (zenon_L4_ : ((op (e1) (e3)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> False). % 3.86/4.02 do 0 intro. intros zenon_H27 zenon_H28 zenon_H29. % 3.86/4.02 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H2a | zenon_intro zenon_H2b ]. % 3.86/4.02 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e1) (e0)) = (op (e1) (e3)))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_H29. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H2a. % 3.86/4.02 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 3.86/4.02 cut (((op (e1) (e3)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2c]. % 3.86/4.02 congruence. % 3.86/4.02 cut (((op (e1) (e3)) = (e1)) = ((op (e1) (e3)) = (op (e1) (e0)))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_H2c. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H27. % 3.86/4.02 cut (((e1) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2d]. % 3.86/4.02 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 3.86/4.02 congruence. % 3.86/4.02 apply zenon_H2b. apply refl_equal. % 3.86/4.02 apply zenon_H2d. apply sym_equal. exact zenon_H28. % 3.86/4.02 apply zenon_H2b. apply refl_equal. % 3.86/4.02 apply zenon_H2b. apply refl_equal. % 3.86/4.02 (* end of lemma zenon_L4_ *) % 3.86/4.02 assert (zenon_L5_ : (((op (e1) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> False). % 3.86/4.02 do 0 intro. intros zenon_H2e zenon_H28 zenon_H29. % 3.86/4.02 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H27. zenon_intro zenon_H2f. % 3.86/4.02 apply (zenon_L4_); trivial. % 3.86/4.02 (* end of lemma zenon_L5_ *) % 3.86/4.02 assert (zenon_L6_ : (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> False). % 3.86/4.02 do 0 intro. intros zenon_H30 zenon_H31 zenon_H32. % 3.86/4.02 cut (((op (e2) (e1)) = (e2)) = ((op (e2) (e1)) = (op (e2) (e3)))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_H30. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H31. % 3.86/4.02 cut (((e2) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 3.86/4.02 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 3.86/4.02 congruence. % 3.86/4.02 apply zenon_H34. apply refl_equal. % 3.86/4.02 apply zenon_H33. apply sym_equal. exact zenon_H32. % 3.86/4.02 (* end of lemma zenon_L6_ *) % 3.86/4.02 assert (zenon_L7_ : (((op (e2) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 3.86/4.02 do 0 intro. intros zenon_H35 zenon_H31 zenon_H30. % 3.86/4.02 apply (zenon_and_s _ _ zenon_H35). zenon_intro zenon_H32. zenon_intro zenon_H36. % 3.86/4.02 apply (zenon_L6_); trivial. % 3.86/4.02 (* end of lemma zenon_L7_ *) % 3.86/4.02 assert (zenon_L8_ : (((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))) -> False). % 3.86/4.02 do 0 intro. intros zenon_H37. % 3.86/4.02 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_H39. zenon_intro zenon_H38. % 3.86/4.02 exact (zenon_H38 zenon_H39). % 3.86/4.02 (* end of lemma zenon_L8_ *) % 3.86/4.02 assert (zenon_L9_ : (((op (e1) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2)))) -> (~((op (e1) (e2)) = (e1))) -> False). % 3.86/4.02 do 0 intro. intros zenon_H3a zenon_H3b. % 3.86/4.02 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H3d. zenon_intro zenon_H3c. % 3.86/4.02 exact (zenon_H3b zenon_H3d). % 3.86/4.02 (* end of lemma zenon_L9_ *) % 3.86/4.02 assert (zenon_L10_ : (((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))) -> False). % 3.86/4.02 do 0 intro. intros zenon_H3e. % 3.86/4.02 apply (zenon_and_s _ _ zenon_H3e). zenon_intro zenon_H40. zenon_intro zenon_H3f. % 3.86/4.02 exact (zenon_H3f zenon_H40). % 3.86/4.02 (* end of lemma zenon_L10_ *) % 3.86/4.02 assert (zenon_L11_ : ((op (e1) (e0)) = (e1)) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> False). % 3.86/4.02 do 0 intro. intros zenon_H28 zenon_H41 zenon_H42. % 3.86/4.02 elim (classic ((op (e1) (e0)) = (op (e1) (e0)))); [ zenon_intro zenon_H43 | zenon_intro zenon_H44 ]. % 3.86/4.02 cut (((op (e1) (e0)) = (op (e1) (e0))) = ((op (e0) (e0)) = (op (e1) (e0)))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_H42. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H43. % 3.86/4.02 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H44]. % 3.86/4.02 cut (((op (e1) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H45]. % 3.86/4.02 congruence. % 3.86/4.02 cut (((op (e1) (e0)) = (e1)) = ((op (e1) (e0)) = (op (e0) (e0)))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_H45. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H28. % 3.86/4.02 cut (((e1) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 3.86/4.02 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H44]. % 3.86/4.02 congruence. % 3.86/4.02 apply zenon_H44. apply refl_equal. % 3.86/4.02 apply zenon_H46. apply sym_equal. exact zenon_H41. % 3.86/4.02 apply zenon_H44. apply refl_equal. % 3.86/4.02 apply zenon_H44. apply refl_equal. % 3.86/4.02 (* end of lemma zenon_L11_ *) % 3.86/4.02 assert (zenon_L12_ : (~((e0) = (e0))) -> False). % 3.86/4.02 do 0 intro. intros zenon_H47. % 3.86/4.02 apply zenon_H47. apply refl_equal. % 3.86/4.02 (* end of lemma zenon_L12_ *) % 3.86/4.02 assert (zenon_L13_ : ((op (e2) (e0)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> (~((e0) = (e1))) -> False). % 3.86/4.02 do 0 intro. intros zenon_H48 zenon_H49 zenon_H4a. % 3.86/4.02 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H4b | zenon_intro zenon_H4c ]. % 3.86/4.02 cut (((e1) = (e1)) = ((e0) = (e1))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_H4a. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H4b. % 3.86/4.02 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 3.86/4.02 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 3.86/4.02 congruence. % 3.86/4.02 cut (((op (e2) (e0)) = (e0)) = ((e1) = (e0))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_H4d. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H48. % 3.86/4.02 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H47]. % 3.86/4.02 cut (((op (e2) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 3.86/4.02 congruence. % 3.86/4.02 exact (zenon_H4e zenon_H49). % 3.86/4.02 apply zenon_H47. apply refl_equal. % 3.86/4.02 apply zenon_H4c. apply refl_equal. % 3.86/4.02 apply zenon_H4c. apply refl_equal. % 3.86/4.02 (* end of lemma zenon_L13_ *) % 3.86/4.02 assert (zenon_L14_ : (~((e2) = (e2))) -> False). % 3.86/4.02 do 0 intro. intros zenon_H4f. % 3.86/4.02 apply zenon_H4f. apply refl_equal. % 3.86/4.02 (* end of lemma zenon_L14_ *) % 3.86/4.02 assert (zenon_L15_ : (~((e1) = (e2))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (e1)) = (e1)) -> False). % 3.86/4.02 do 0 intro. intros zenon_H50 zenon_H31 zenon_H51. % 3.86/4.02 cut (((op (e2) (e1)) = (e2)) = ((e1) = (e2))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_H50. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H31. % 3.86/4.02 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 3.86/4.02 cut (((op (e2) (e1)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 3.86/4.02 congruence. % 3.86/4.02 exact (zenon_H52 zenon_H51). % 3.86/4.02 apply zenon_H4f. apply refl_equal. % 3.86/4.02 (* end of lemma zenon_L15_ *) % 3.86/4.02 assert (zenon_L16_ : (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e3) (e0)) = (e1)) -> False). % 3.86/4.02 do 0 intro. intros zenon_H53 zenon_H28 zenon_H54. % 3.86/4.02 cut (((op (e1) (e0)) = (e1)) = ((op (e1) (e0)) = (op (e3) (e0)))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_H53. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H28. % 3.86/4.02 cut (((e1) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H55]. % 3.86/4.02 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H44]. % 3.86/4.02 congruence. % 3.86/4.02 apply zenon_H44. apply refl_equal. % 3.86/4.02 apply zenon_H55. apply sym_equal. exact zenon_H54. % 3.86/4.02 (* end of lemma zenon_L16_ *) % 3.86/4.02 assert (zenon_L17_ : (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e3) (e1)) = (e1)) -> False). % 3.86/4.02 do 0 intro. intros zenon_H56 zenon_H57 zenon_H58. % 3.86/4.02 cut (((op (e0) (e1)) = (e1)) = ((op (e0) (e1)) = (op (e3) (e1)))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_H56. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H57. % 3.86/4.02 cut (((e1) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 3.86/4.02 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 3.86/4.02 congruence. % 3.86/4.02 apply zenon_H5a. apply refl_equal. % 3.86/4.02 apply zenon_H59. apply sym_equal. exact zenon_H58. % 3.86/4.02 (* end of lemma zenon_L17_ *) % 3.86/4.02 assert (zenon_L18_ : (~((e3) = (e3))) -> False). % 3.86/4.02 do 0 intro. intros zenon_H5b. % 3.86/4.02 apply zenon_H5b. apply refl_equal. % 3.86/4.02 (* end of lemma zenon_L18_ *) % 3.86/4.02 assert (zenon_L19_ : (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e2)) = (e1)) -> False). % 3.86/4.02 do 0 intro. intros zenon_H5c zenon_H5d zenon_H5e. % 3.86/4.02 cut (((op (e3) (e2)) = (e3)) = ((e1) = (e3))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_H5c. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H5d. % 3.86/4.02 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H5b]. % 3.86/4.02 cut (((op (e3) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H5f]. % 3.86/4.02 congruence. % 3.86/4.02 exact (zenon_H5f zenon_H5e). % 3.86/4.02 apply zenon_H5b. apply refl_equal. % 3.86/4.02 (* end of lemma zenon_L19_ *) % 3.86/4.02 assert (zenon_L20_ : ((op (e0) (e3)) = (e0)) -> ((op (e0) (e3)) = (e2)) -> (~((e0) = (e2))) -> False). % 3.86/4.02 do 0 intro. intros zenon_H22 zenon_H60 zenon_H61. % 3.86/4.02 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H62 | zenon_intro zenon_H4f ]. % 3.86/4.02 cut (((e2) = (e2)) = ((e0) = (e2))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_H61. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H62. % 3.86/4.02 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 3.86/4.02 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H63]. % 3.86/4.02 congruence. % 3.86/4.02 cut (((op (e0) (e3)) = (e0)) = ((e2) = (e0))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_H63. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H22. % 3.86/4.02 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H47]. % 3.86/4.02 cut (((op (e0) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H64]. % 3.86/4.02 congruence. % 3.86/4.02 exact (zenon_H64 zenon_H60). % 3.86/4.02 apply zenon_H47. apply refl_equal. % 3.86/4.02 apply zenon_H4f. apply refl_equal. % 3.86/4.02 apply zenon_H4f. apply refl_equal. % 3.86/4.02 (* end of lemma zenon_L20_ *) % 3.86/4.02 assert (zenon_L21_ : (~((op (op (e0) (e0)) (op (e0) (e0))) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> False). % 3.86/4.02 do 0 intro. intros zenon_H65 zenon_H66. % 3.86/4.02 cut (((op (e0) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 3.86/4.02 cut (((op (e0) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 3.86/4.02 congruence. % 3.86/4.02 exact (zenon_H67 zenon_H66). % 3.86/4.02 exact (zenon_H67 zenon_H66). % 3.86/4.02 (* end of lemma zenon_L21_ *) % 3.86/4.02 assert (zenon_L22_ : (~((e1) = (e1))) -> False). % 3.86/4.02 do 0 intro. intros zenon_H4c. % 3.86/4.02 apply zenon_H4c. apply refl_equal. % 3.86/4.02 (* end of lemma zenon_L22_ *) % 3.86/4.02 assert (zenon_L23_ : ((op (e3) (e3)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> False). % 3.86/4.02 do 0 intro. intros zenon_H68 zenon_H69 zenon_H66. % 3.86/4.02 apply (zenon_notand_s _ _ ax14); [ zenon_intro zenon_H6b | zenon_intro zenon_H6a ]. % 3.86/4.02 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H6c | zenon_intro zenon_H6d ]. % 3.86/4.02 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((e1) = (op (op (e0) (e0)) (op (e0) (e0))))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_H6b. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H6c. % 3.86/4.02 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 3.86/4.02 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H6e]. % 3.86/4.02 congruence. % 3.86/4.02 cut (((op (e3) (e3)) = (e1)) = ((op (op (e0) (e0)) (op (e0) (e0))) = (e1))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_H6e. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H68. % 3.86/4.02 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 3.86/4.02 cut (((op (e3) (e3)) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 3.86/4.02 congruence. % 3.86/4.02 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H6c | zenon_intro zenon_H6d ]. % 3.86/4.02 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((op (e3) (e3)) = (op (op (e0) (e0)) (op (e0) (e0))))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_H6f. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H6c. % 3.86/4.02 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 3.86/4.02 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 3.86/4.02 congruence. % 3.86/4.02 apply (zenon_L21_); trivial. % 3.86/4.02 apply zenon_H6d. apply refl_equal. % 3.86/4.02 apply zenon_H6d. apply refl_equal. % 3.86/4.02 apply zenon_H4c. apply refl_equal. % 3.86/4.02 apply zenon_H6d. apply refl_equal. % 3.86/4.02 apply zenon_H6d. apply refl_equal. % 3.86/4.02 apply (zenon_notand_s _ _ zenon_H6a); [ zenon_intro zenon_H71 | zenon_intro zenon_H70 ]. % 3.86/4.02 elim (classic ((op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))))); [ zenon_intro zenon_H72 | zenon_intro zenon_H73 ]. % 3.86/4.02 cut (((op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) = ((e2) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_H71. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H72. % 3.86/4.02 cut (((op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 3.86/4.02 cut (((op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H74]. % 3.86/4.02 congruence. % 3.86/4.02 cut (((op (e1) (e3)) = (e2)) = ((op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))) = (e2))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_H74. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H69. % 3.86/4.02 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 3.86/4.02 cut (((op (e1) (e3)) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H75]. % 3.86/4.02 congruence. % 3.86/4.02 elim (classic ((op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))))); [ zenon_intro zenon_H72 | zenon_intro zenon_H73 ]. % 3.86/4.02 cut (((op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) = ((op (e1) (e3)) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_H75. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H72. % 3.86/4.02 cut (((op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 3.86/4.02 cut (((op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H76]. % 3.86/4.02 congruence. % 3.86/4.02 cut (((op (e0) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 3.86/4.02 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H6e]. % 3.86/4.02 congruence. % 3.86/4.02 cut (((op (e3) (e3)) = (e1)) = ((op (op (e0) (e0)) (op (e0) (e0))) = (e1))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_H6e. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H68. % 3.86/4.02 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 3.86/4.02 cut (((op (e3) (e3)) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 3.86/4.02 congruence. % 3.86/4.02 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H6c | zenon_intro zenon_H6d ]. % 3.86/4.02 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((op (e3) (e3)) = (op (op (e0) (e0)) (op (e0) (e0))))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_H6f. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H6c. % 3.86/4.02 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 3.86/4.02 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 3.86/4.02 congruence. % 3.86/4.02 apply (zenon_L21_); trivial. % 3.86/4.02 apply zenon_H6d. apply refl_equal. % 3.86/4.02 apply zenon_H6d. apply refl_equal. % 3.86/4.02 apply zenon_H4c. apply refl_equal. % 3.86/4.02 exact (zenon_H67 zenon_H66). % 3.86/4.02 apply zenon_H73. apply refl_equal. % 3.86/4.02 apply zenon_H73. apply refl_equal. % 3.86/4.02 apply zenon_H4f. apply refl_equal. % 3.86/4.02 apply zenon_H73. apply refl_equal. % 3.86/4.02 apply zenon_H73. apply refl_equal. % 3.86/4.02 apply zenon_H70. apply sym_equal. exact zenon_H66. % 3.86/4.02 (* end of lemma zenon_L23_ *) % 3.86/4.02 assert (zenon_L24_ : (~((op (op (e3) (e3)) (op (e3) (e3))) = (op (e2) (e2)))) -> ((op (e3) (e3)) = (e2)) -> False). % 3.86/4.02 do 0 intro. intros zenon_H77 zenon_H78. % 3.86/4.02 cut (((op (e3) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 3.86/4.02 cut (((op (e3) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 3.86/4.02 congruence. % 3.86/4.02 exact (zenon_H79 zenon_H78). % 3.86/4.02 exact (zenon_H79 zenon_H78). % 3.86/4.02 (* end of lemma zenon_L24_ *) % 3.86/4.02 assert (zenon_L25_ : ((op (e2) (e2)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> (~((e1) = (op (op (e3) (e3)) (op (e3) (e3))))) -> False). % 3.86/4.02 do 0 intro. intros zenon_H7a zenon_H78 zenon_H7b. % 3.86/4.02 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H7c | zenon_intro zenon_H7d ]. % 3.86/4.02 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((e1) = (op (op (e3) (e3)) (op (e3) (e3))))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_H7b. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H7c. % 3.86/4.02 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H7d]. % 3.86/4.02 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 3.86/4.02 congruence. % 3.86/4.02 cut (((op (e2) (e2)) = (e1)) = ((op (op (e3) (e3)) (op (e3) (e3))) = (e1))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_H7e. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H7a. % 3.86/4.02 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 3.86/4.02 cut (((op (e2) (e2)) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H7f]. % 3.86/4.02 congruence. % 3.86/4.02 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H7c | zenon_intro zenon_H7d ]. % 3.86/4.02 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((op (e2) (e2)) = (op (op (e3) (e3)) (op (e3) (e3))))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_H7f. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H7c. % 3.86/4.02 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H7d]. % 3.86/4.02 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H77]. % 3.86/4.02 congruence. % 3.86/4.02 apply (zenon_L24_); trivial. % 3.86/4.02 apply zenon_H7d. apply refl_equal. % 3.86/4.02 apply zenon_H7d. apply refl_equal. % 3.86/4.02 apply zenon_H4c. apply refl_equal. % 3.86/4.02 apply zenon_H7d. apply refl_equal. % 3.86/4.02 apply zenon_H7d. apply refl_equal. % 3.86/4.02 (* end of lemma zenon_L25_ *) % 3.86/4.02 assert (zenon_L26_ : ((op (e2) (e2)) = (e1)) -> ((op (e1) (e2)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> False). % 3.86/4.02 do 0 intro. intros zenon_H7a zenon_H80 zenon_H78. % 3.86/4.02 apply (zenon_notand_s _ _ ax13); [ zenon_intro zenon_H7b | zenon_intro zenon_H81 ]. % 3.86/4.02 apply (zenon_L25_); trivial. % 3.86/4.02 apply (zenon_notand_s _ _ zenon_H81); [ zenon_intro zenon_H83 | zenon_intro zenon_H82 ]. % 3.86/4.02 elim (classic ((op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))))); [ zenon_intro zenon_H84 | zenon_intro zenon_H85 ]. % 3.86/4.02 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) = ((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_H83. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H84. % 3.86/4.02 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 3.86/4.02 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H86]. % 3.86/4.02 congruence. % 3.86/4.02 cut (((op (e1) (e2)) = (e0)) = ((op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))) = (e0))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_H86. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H80. % 3.86/4.02 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H47]. % 3.86/4.02 cut (((op (e1) (e2)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 3.86/4.02 congruence. % 3.86/4.02 elim (classic ((op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))))); [ zenon_intro zenon_H84 | zenon_intro zenon_H85 ]. % 3.86/4.02 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) = ((op (e1) (e2)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_H87. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H84. % 3.86/4.02 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 3.86/4.02 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H88]. % 3.86/4.02 congruence. % 3.86/4.02 cut (((op (e3) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 3.86/4.02 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 3.86/4.02 congruence. % 3.86/4.02 cut (((op (e2) (e2)) = (e1)) = ((op (op (e3) (e3)) (op (e3) (e3))) = (e1))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_H7e. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H7a. % 3.86/4.02 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 3.86/4.02 cut (((op (e2) (e2)) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H7f]. % 3.86/4.02 congruence. % 3.86/4.02 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H7c | zenon_intro zenon_H7d ]. % 3.86/4.02 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((op (e2) (e2)) = (op (op (e3) (e3)) (op (e3) (e3))))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_H7f. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H7c. % 3.86/4.02 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H7d]. % 3.86/4.02 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H77]. % 3.86/4.02 congruence. % 3.86/4.02 apply (zenon_L24_); trivial. % 3.86/4.02 apply zenon_H7d. apply refl_equal. % 3.86/4.02 apply zenon_H7d. apply refl_equal. % 3.86/4.02 apply zenon_H4c. apply refl_equal. % 3.86/4.02 exact (zenon_H79 zenon_H78). % 3.86/4.02 apply zenon_H85. apply refl_equal. % 3.86/4.02 apply zenon_H85. apply refl_equal. % 3.86/4.02 apply zenon_H47. apply refl_equal. % 3.86/4.02 apply zenon_H85. apply refl_equal. % 3.86/4.02 apply zenon_H85. apply refl_equal. % 3.86/4.02 apply zenon_H82. apply sym_equal. exact zenon_H78. % 3.86/4.02 (* end of lemma zenon_L26_ *) % 3.86/4.02 assert (zenon_L27_ : (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e1)) -> ((op (e3) (e3)) = (e1)) -> False). % 3.86/4.02 do 0 intro. intros zenon_H89 zenon_H8a zenon_H68. % 3.86/4.02 cut (((op (e2) (e3)) = (e1)) = ((op (e2) (e3)) = (op (e3) (e3)))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_H89. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H8a. % 3.86/4.02 cut (((e1) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 3.86/4.02 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H8c]. % 3.86/4.02 congruence. % 3.86/4.02 apply zenon_H8c. apply refl_equal. % 3.86/4.02 apply zenon_H8b. apply sym_equal. exact zenon_H68. % 3.86/4.02 (* end of lemma zenon_L27_ *) % 3.86/4.02 assert (zenon_L28_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e1)) -> False). % 3.86/4.02 do 0 intro. intros zenon_H8d zenon_H28 zenon_H53 zenon_H57 zenon_H56 zenon_H5d zenon_H5c zenon_H89 zenon_H8a. % 3.86/4.02 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H54 | zenon_intro zenon_H8e ]. % 3.86/4.02 apply (zenon_L16_); trivial. % 3.86/4.02 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H58 | zenon_intro zenon_H8f ]. % 3.86/4.02 apply (zenon_L17_); trivial. % 3.86/4.02 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H5e | zenon_intro zenon_H68 ]. % 3.86/4.02 apply (zenon_L19_); trivial. % 3.86/4.02 apply (zenon_L27_); trivial. % 3.86/4.02 (* end of lemma zenon_L28_ *) % 3.86/4.02 assert (zenon_L29_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e2) (e3)) = (e2))) -> ((op (e0) (e0)) = (e3)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 3.86/4.02 do 0 intro. intros zenon_H90 zenon_H4a zenon_H48 zenon_H31 zenon_H50 zenon_H80 zenon_H91 zenon_H66 zenon_H22 zenon_H61 zenon_H92 zenon_H8d zenon_H28 zenon_H53 zenon_H57 zenon_H56 zenon_H5d zenon_H5c zenon_H89. % 3.86/4.02 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H49 | zenon_intro zenon_H93 ]. % 3.86/4.02 apply (zenon_L13_); trivial. % 3.86/4.02 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H51 | zenon_intro zenon_H94 ]. % 3.86/4.02 apply (zenon_L15_); trivial. % 3.86/4.02 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H7a | zenon_intro zenon_H8a ]. % 3.86/4.02 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H54 | zenon_intro zenon_H8e ]. % 3.86/4.02 apply (zenon_L16_); trivial. % 3.86/4.02 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H58 | zenon_intro zenon_H8f ]. % 3.86/4.02 apply (zenon_L17_); trivial. % 3.86/4.02 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H5e | zenon_intro zenon_H68 ]. % 3.86/4.02 apply (zenon_L19_); trivial. % 3.86/4.02 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H60 | zenon_intro zenon_H95 ]. % 3.86/4.02 apply (zenon_L20_); trivial. % 3.86/4.02 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H69 | zenon_intro zenon_H96 ]. % 3.86/4.02 apply (zenon_L23_); trivial. % 3.86/4.02 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H32 | zenon_intro zenon_H78 ]. % 3.86/4.02 exact (zenon_H91 zenon_H32). % 3.86/4.02 apply (zenon_L26_); trivial. % 3.86/4.02 apply (zenon_L28_); trivial. % 3.86/4.02 (* end of lemma zenon_L29_ *) % 3.86/4.02 assert (zenon_L30_ : (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e2) (e2)) = (e0)) -> False). % 3.86/4.02 do 0 intro. intros zenon_H97 zenon_H48 zenon_H98. % 3.86/4.02 cut (((op (e2) (e0)) = (e0)) = ((op (e2) (e0)) = (op (e2) (e2)))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_H97. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H48. % 3.86/4.02 cut (((e0) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H99]. % 3.86/4.02 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 3.86/4.02 congruence. % 3.86/4.02 apply zenon_H9a. apply refl_equal. % 3.86/4.02 apply zenon_H99. apply sym_equal. exact zenon_H98. % 3.86/4.02 (* end of lemma zenon_L30_ *) % 3.86/4.02 assert (zenon_L31_ : (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e2)) = (e0)) -> False). % 3.86/4.02 do 0 intro. intros zenon_H9b zenon_H5d zenon_H9c. % 3.86/4.02 cut (((op (e3) (e2)) = (e3)) = ((e0) = (e3))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_H9b. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H5d. % 3.86/4.02 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H5b]. % 3.86/4.02 cut (((op (e3) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H9d]. % 3.86/4.02 congruence. % 3.86/4.02 exact (zenon_H9d zenon_H9c). % 3.86/4.02 apply zenon_H5b. apply refl_equal. % 3.86/4.02 (* end of lemma zenon_L31_ *) % 3.86/4.02 assert (zenon_L32_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e2) (e3)) = (e2))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 3.86/4.02 do 0 intro. intros zenon_H9e zenon_H20 zenon_H89 zenon_H5c zenon_H56 zenon_H57 zenon_H53 zenon_H28 zenon_H8d zenon_H92 zenon_H61 zenon_H22 zenon_H66 zenon_H91 zenon_H50 zenon_H31 zenon_H4a zenon_H90 zenon_H48 zenon_H97 zenon_H9b zenon_H5d. % 3.86/4.02 apply (zenon_or_s _ _ zenon_H9e); [ zenon_intro zenon_H21 | zenon_intro zenon_H9f ]. % 3.86/4.02 apply (zenon_L2_); trivial. % 3.86/4.02 apply (zenon_or_s _ _ zenon_H9f); [ zenon_intro zenon_H80 | zenon_intro zenon_Ha0 ]. % 3.86/4.02 apply (zenon_L29_); trivial. % 3.86/4.02 apply (zenon_or_s _ _ zenon_Ha0); [ zenon_intro zenon_H98 | zenon_intro zenon_H9c ]. % 3.86/4.02 apply (zenon_L30_); trivial. % 3.86/4.02 apply (zenon_L31_); trivial. % 3.86/4.02 (* end of lemma zenon_L32_ *) % 3.86/4.02 assert (zenon_L33_ : (~((e0) = (e2))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (e1)) = (e0)) -> False). % 3.86/4.02 do 0 intro. intros zenon_H61 zenon_H31 zenon_Ha1. % 3.86/4.02 cut (((op (e2) (e1)) = (e2)) = ((e0) = (e2))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_H61. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H31. % 3.86/4.02 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 3.86/4.02 cut (((op (e2) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 3.86/4.02 congruence. % 3.86/4.02 exact (zenon_Ha2 zenon_Ha1). % 3.86/4.02 apply zenon_H4f. apply refl_equal. % 3.86/4.02 (* end of lemma zenon_L33_ *) % 3.86/4.02 assert (zenon_L34_ : (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e2) (e2)) = (e0)) -> False). % 3.86/4.02 do 0 intro. intros zenon_Ha3 zenon_H21 zenon_H98. % 3.86/4.02 cut (((op (e0) (e2)) = (e0)) = ((op (e0) (e2)) = (op (e2) (e2)))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_Ha3. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H21. % 3.86/4.02 cut (((e0) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H99]. % 3.86/4.02 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H24]. % 3.86/4.02 congruence. % 3.86/4.02 apply zenon_H24. apply refl_equal. % 3.86/4.02 apply zenon_H99. apply sym_equal. exact zenon_H98. % 3.86/4.02 (* end of lemma zenon_L34_ *) % 3.86/4.02 assert (zenon_L35_ : ((op (e2) (e2)) = (e0)) -> ((op (e0) (e2)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> False). % 3.86/4.02 do 0 intro. intros zenon_H98 zenon_Ha4 zenon_H78. % 3.86/4.02 apply (zenon_notand_s _ _ ax7); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Ha5 ]. % 3.86/4.02 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H7c | zenon_intro zenon_H7d ]. % 3.86/4.02 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((e0) = (op (op (e3) (e3)) (op (e3) (e3))))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_Ha6. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H7c. % 3.86/4.02 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H7d]. % 3.86/4.02 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Ha7]. % 3.86/4.02 congruence. % 3.86/4.02 cut (((op (e2) (e2)) = (e0)) = ((op (op (e3) (e3)) (op (e3) (e3))) = (e0))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_Ha7. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H98. % 3.86/4.02 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H47]. % 3.86/4.02 cut (((op (e2) (e2)) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H7f]. % 3.86/4.02 congruence. % 3.86/4.02 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H7c | zenon_intro zenon_H7d ]. % 3.86/4.02 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((op (e2) (e2)) = (op (op (e3) (e3)) (op (e3) (e3))))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_H7f. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H7c. % 3.86/4.02 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H7d]. % 3.86/4.02 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H77]. % 3.86/4.02 congruence. % 3.86/4.02 apply (zenon_L24_); trivial. % 3.86/4.02 apply zenon_H7d. apply refl_equal. % 3.86/4.02 apply zenon_H7d. apply refl_equal. % 3.86/4.02 apply zenon_H47. apply refl_equal. % 3.86/4.02 apply zenon_H7d. apply refl_equal. % 3.86/4.02 apply zenon_H7d. apply refl_equal. % 3.86/4.02 apply (zenon_notand_s _ _ zenon_Ha5); [ zenon_intro zenon_Ha8 | zenon_intro zenon_H82 ]. % 3.86/4.02 elim (classic ((op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))))); [ zenon_intro zenon_H84 | zenon_intro zenon_H85 ]. % 3.86/4.02 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) = ((e1) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_Ha8. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H84. % 3.86/4.02 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 3.86/4.02 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Ha9]. % 3.86/4.02 congruence. % 3.86/4.02 cut (((op (e0) (e2)) = (e1)) = ((op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))) = (e1))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_Ha9. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_Ha4. % 3.86/4.02 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 3.86/4.02 cut (((op (e0) (e2)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_Haa]. % 3.86/4.02 congruence. % 3.86/4.02 elim (classic ((op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))))); [ zenon_intro zenon_H84 | zenon_intro zenon_H85 ]. % 3.86/4.02 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) = ((op (e0) (e2)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_Haa. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H84. % 3.86/4.02 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 3.86/4.02 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 3.86/4.02 congruence. % 3.86/4.02 cut (((op (e3) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 3.86/4.02 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Ha7]. % 3.86/4.02 congruence. % 3.86/4.02 cut (((op (e2) (e2)) = (e0)) = ((op (op (e3) (e3)) (op (e3) (e3))) = (e0))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_Ha7. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H98. % 3.86/4.02 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H47]. % 3.86/4.02 cut (((op (e2) (e2)) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H7f]. % 3.86/4.02 congruence. % 3.86/4.02 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H7c | zenon_intro zenon_H7d ]. % 3.86/4.02 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((op (e2) (e2)) = (op (op (e3) (e3)) (op (e3) (e3))))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_H7f. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H7c. % 3.86/4.02 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H7d]. % 3.86/4.02 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H77]. % 3.86/4.02 congruence. % 3.86/4.02 apply (zenon_L24_); trivial. % 3.86/4.02 apply zenon_H7d. apply refl_equal. % 3.86/4.02 apply zenon_H7d. apply refl_equal. % 3.86/4.02 apply zenon_H47. apply refl_equal. % 3.86/4.02 exact (zenon_H79 zenon_H78). % 3.86/4.02 apply zenon_H85. apply refl_equal. % 3.86/4.02 apply zenon_H85. apply refl_equal. % 3.86/4.02 apply zenon_H4c. apply refl_equal. % 3.86/4.02 apply zenon_H85. apply refl_equal. % 3.86/4.02 apply zenon_H85. apply refl_equal. % 3.86/4.02 apply zenon_H82. apply sym_equal. exact zenon_H78. % 3.86/4.02 (* end of lemma zenon_L35_ *) % 3.86/4.02 assert (zenon_L36_ : (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e0)) -> ((op (e2) (e2)) = (e0)) -> False). % 3.86/4.02 do 0 intro. intros zenon_Hac zenon_H80 zenon_H98. % 3.86/4.02 cut (((op (e1) (e2)) = (e0)) = ((op (e1) (e2)) = (op (e2) (e2)))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_Hac. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H80. % 3.86/4.02 cut (((e0) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H99]. % 3.86/4.02 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Had]. % 3.86/4.02 congruence. % 3.86/4.02 apply zenon_Had. apply refl_equal. % 3.86/4.02 apply zenon_H99. apply sym_equal. exact zenon_H98. % 3.86/4.02 (* end of lemma zenon_L36_ *) % 3.86/4.02 assert (zenon_L37_ : (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e2)) = (e2)) -> False). % 3.86/4.02 do 0 intro. intros zenon_Hae zenon_Haf zenon_Hb0. % 3.86/4.02 cut (((op (e0) (e2)) = (e2)) = ((op (e0) (e2)) = (op (e1) (e2)))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_Hae. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_Haf. % 3.86/4.02 cut (((e2) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hb1]. % 3.86/4.02 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H24]. % 3.86/4.02 congruence. % 3.86/4.02 apply zenon_H24. apply refl_equal. % 3.86/4.02 apply zenon_Hb1. apply sym_equal. exact zenon_Hb0. % 3.86/4.02 (* end of lemma zenon_L37_ *) % 3.86/4.02 assert (zenon_L38_ : ((op (e3) (e2)) = (e3)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 3.86/4.02 do 0 intro. intros zenon_H5d zenon_Hb2 zenon_Hb3. % 3.86/4.02 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hb5 ]. % 3.86/4.02 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e1) (e2)) = (op (e3) (e2)))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_Hb3. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_Hb4. % 3.86/4.02 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hb5]. % 3.86/4.02 cut (((op (e3) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 3.86/4.02 congruence. % 3.86/4.02 cut (((op (e3) (e2)) = (e3)) = ((op (e3) (e2)) = (op (e1) (e2)))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_Hb6. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H5d. % 3.86/4.02 cut (((e3) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hb7]. % 3.86/4.02 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hb5]. % 3.86/4.02 congruence. % 3.86/4.02 apply zenon_Hb5. apply refl_equal. % 3.86/4.02 apply zenon_Hb7. apply sym_equal. exact zenon_Hb2. % 3.86/4.02 apply zenon_Hb5. apply refl_equal. % 3.86/4.02 apply zenon_Hb5. apply refl_equal. % 3.86/4.02 (* end of lemma zenon_L38_ *) % 3.86/4.02 assert (zenon_L39_ : (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (e1))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 3.86/4.02 do 0 intro. intros zenon_Hb8 zenon_H98 zenon_Hac zenon_H3b zenon_Haf zenon_Hae zenon_H5d zenon_Hb3. % 3.86/4.02 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H80 | zenon_intro zenon_Hb9 ]. % 3.86/4.02 apply (zenon_L36_); trivial. % 3.86/4.02 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_H3d | zenon_intro zenon_Hba ]. % 3.86/4.02 exact (zenon_H3b zenon_H3d). % 3.86/4.02 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hb2 ]. % 3.86/4.02 apply (zenon_L37_); trivial. % 3.86/4.02 apply (zenon_L38_); trivial. % 3.86/4.02 (* end of lemma zenon_L39_ *) % 3.86/4.02 assert (zenon_L40_ : ((op (e3) (e2)) = (e3)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> False). % 3.86/4.02 do 0 intro. intros zenon_H5d zenon_Hbb zenon_Hbc. % 3.86/4.02 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hb5 ]. % 3.86/4.02 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e0) (e2)) = (op (e3) (e2)))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_Hbc. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_Hb4. % 3.86/4.02 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hb5]. % 3.86/4.02 cut (((op (e3) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hbd]. % 3.86/4.02 congruence. % 3.86/4.02 cut (((op (e3) (e2)) = (e3)) = ((op (e3) (e2)) = (op (e0) (e2)))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_Hbd. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H5d. % 3.86/4.02 cut (((e3) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hbe]. % 3.86/4.02 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hb5]. % 3.86/4.02 congruence. % 3.86/4.02 apply zenon_Hb5. apply refl_equal. % 3.86/4.02 apply zenon_Hbe. apply sym_equal. exact zenon_Hbb. % 3.86/4.02 apply zenon_Hb5. apply refl_equal. % 3.86/4.02 apply zenon_Hb5. apply refl_equal. % 3.86/4.02 (* end of lemma zenon_L40_ *) % 3.86/4.02 assert (zenon_L41_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> False). % 3.86/4.02 do 0 intro. intros zenon_Hbf zenon_Ha3 zenon_H78 zenon_Hb3 zenon_Hae zenon_H3b zenon_Hac zenon_H98 zenon_Hb8 zenon_H5d zenon_Hbc. % 3.86/4.02 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H21 | zenon_intro zenon_Hc0 ]. % 3.86/4.02 apply (zenon_L34_); trivial. % 3.86/4.02 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Ha4 | zenon_intro zenon_Hc1 ]. % 3.86/4.02 apply (zenon_L35_); trivial. % 3.86/4.02 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_Haf | zenon_intro zenon_Hbb ]. % 3.86/4.02 apply (zenon_L39_); trivial. % 3.86/4.02 apply (zenon_L40_); trivial. % 3.86/4.02 (* end of lemma zenon_L41_ *) % 3.86/4.02 assert (zenon_L42_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e2) (e3)) = (e0)) -> False). % 3.86/4.02 do 0 intro. intros zenon_Hc2 zenon_H22 zenon_Hc3. % 3.86/4.02 cut (((op (e0) (e3)) = (e0)) = ((op (e0) (e3)) = (op (e2) (e3)))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_Hc2. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H22. % 3.86/4.02 cut (((e0) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hc4]. % 3.86/4.02 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 3.86/4.02 congruence. % 3.86/4.02 apply zenon_Hc5. apply refl_equal. % 3.86/4.02 apply zenon_Hc4. apply sym_equal. exact zenon_Hc3. % 3.86/4.02 (* end of lemma zenon_L42_ *) % 3.86/4.02 assert (zenon_L43_ : ((op (e0) (e1)) = (e1)) -> ((op (e0) (e1)) = (e3)) -> (~((e1) = (e3))) -> False). % 3.86/4.02 do 0 intro. intros zenon_H57 zenon_Hc6 zenon_H5c. % 3.86/4.02 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H5b ]. % 3.86/4.02 cut (((e3) = (e3)) = ((e1) = (e3))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_H5c. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_Hc7. % 3.86/4.02 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H5b]. % 3.86/4.02 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hc8]. % 3.86/4.02 congruence. % 3.86/4.02 cut (((op (e0) (e1)) = (e1)) = ((e3) = (e1))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_Hc8. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H57. % 3.86/4.02 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 3.86/4.02 cut (((op (e0) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hc9]. % 3.86/4.02 congruence. % 3.86/4.02 exact (zenon_Hc9 zenon_Hc6). % 3.86/4.02 apply zenon_H4c. apply refl_equal. % 3.86/4.02 apply zenon_H5b. apply refl_equal. % 3.86/4.02 apply zenon_H5b. apply refl_equal. % 3.86/4.02 (* end of lemma zenon_L43_ *) % 3.86/4.02 assert (zenon_L44_ : ((op (e0) (e3)) = (e0)) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e3))) -> False). % 3.86/4.02 do 0 intro. intros zenon_H22 zenon_Hca zenon_H9b. % 3.86/4.02 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H5b ]. % 3.86/4.02 cut (((e3) = (e3)) = ((e0) = (e3))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_H9b. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_Hc7. % 3.86/4.02 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H5b]. % 3.86/4.02 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 3.86/4.02 congruence. % 3.86/4.02 cut (((op (e0) (e3)) = (e0)) = ((e3) = (e0))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_Hcb. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H22. % 3.86/4.02 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H47]. % 3.86/4.02 cut (((op (e0) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hcc]. % 3.86/4.02 congruence. % 3.86/4.02 exact (zenon_Hcc zenon_Hca). % 3.86/4.02 apply zenon_H47. apply refl_equal. % 3.86/4.02 apply zenon_H5b. apply refl_equal. % 3.86/4.02 apply zenon_H5b. apply refl_equal. % 3.86/4.02 (* end of lemma zenon_L44_ *) % 3.86/4.02 assert (zenon_L45_ : (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e2) (e2)) = (e1)) -> False). % 3.86/4.02 do 0 intro. intros zenon_Ha3 zenon_Ha4 zenon_H7a. % 3.86/4.02 cut (((op (e0) (e2)) = (e1)) = ((op (e0) (e2)) = (op (e2) (e2)))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_Ha3. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_Ha4. % 3.86/4.02 cut (((e1) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hcd]. % 3.86/4.02 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H24]. % 3.86/4.02 congruence. % 3.86/4.02 apply zenon_H24. apply refl_equal. % 3.86/4.02 apply zenon_Hcd. apply sym_equal. exact zenon_H7a. % 3.86/4.02 (* end of lemma zenon_L45_ *) % 3.86/4.02 assert (zenon_L46_ : (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (e2)) = (e2)) -> False). % 3.86/4.02 do 0 intro. intros zenon_Hce zenon_H31 zenon_H40. % 3.86/4.02 cut (((op (e2) (e1)) = (e2)) = ((op (e2) (e1)) = (op (e2) (e2)))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_Hce. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H31. % 3.86/4.02 cut (((e2) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hcf]. % 3.86/4.02 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 3.86/4.02 congruence. % 3.86/4.02 apply zenon_H34. apply refl_equal. % 3.86/4.02 apply zenon_Hcf. apply sym_equal. exact zenon_H40. % 3.86/4.02 (* end of lemma zenon_L46_ *) % 3.86/4.02 assert (zenon_L47_ : ((op (e3) (e2)) = (e3)) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 3.86/4.02 do 0 intro. intros zenon_H5d zenon_Hd0 zenon_Hd1. % 3.86/4.02 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hb5 ]. % 3.86/4.02 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e2) (e2)) = (op (e3) (e2)))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_Hd1. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_Hb4. % 3.86/4.02 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hb5]. % 3.86/4.02 cut (((op (e3) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hd2]. % 3.86/4.02 congruence. % 3.86/4.02 cut (((op (e3) (e2)) = (e3)) = ((op (e3) (e2)) = (op (e2) (e2)))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_Hd2. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H5d. % 3.86/4.02 cut (((e3) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hd3]. % 3.86/4.02 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hb5]. % 3.86/4.02 congruence. % 3.86/4.02 apply zenon_Hb5. apply refl_equal. % 3.86/4.02 apply zenon_Hd3. apply sym_equal. exact zenon_Hd0. % 3.86/4.02 apply zenon_Hb5. apply refl_equal. % 3.86/4.02 apply zenon_Hb5. apply refl_equal. % 3.86/4.02 (* end of lemma zenon_L47_ *) % 3.86/4.02 assert (zenon_L48_ : (((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 (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 3.86/4.02 do 0 intro. intros zenon_Hd4 zenon_H48 zenon_H97 zenon_Ha4 zenon_Ha3 zenon_H31 zenon_Hce zenon_H5d zenon_Hd1. % 3.86/4.02 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H98 | zenon_intro zenon_Hd5 ]. % 3.86/4.02 apply (zenon_L30_); trivial. % 3.86/4.02 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H7a | zenon_intro zenon_Hd6 ]. % 3.86/4.02 apply (zenon_L45_); trivial. % 3.86/4.02 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H40 | zenon_intro zenon_Hd0 ]. % 3.86/4.02 apply (zenon_L46_); trivial. % 3.86/4.02 apply (zenon_L47_); trivial. % 3.86/4.02 (* end of lemma zenon_L48_ *) % 3.86/4.02 assert (zenon_L49_ : ((op (e0) (e3)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((e0) = (e1))) -> False). % 3.86/4.02 do 0 intro. intros zenon_H22 zenon_Hd7 zenon_H4a. % 3.86/4.02 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H4b | zenon_intro zenon_H4c ]. % 3.86/4.02 cut (((e1) = (e1)) = ((e0) = (e1))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_H4a. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H4b. % 3.86/4.02 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 3.86/4.02 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 3.86/4.02 congruence. % 3.86/4.02 cut (((op (e0) (e3)) = (e0)) = ((e1) = (e0))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_H4d. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H22. % 3.86/4.02 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H47]. % 3.86/4.02 cut (((op (e0) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hd8]. % 3.86/4.02 congruence. % 3.86/4.02 exact (zenon_Hd8 zenon_Hd7). % 3.86/4.02 apply zenon_H47. apply refl_equal. % 3.86/4.02 apply zenon_H4c. apply refl_equal. % 3.86/4.02 apply zenon_H4c. apply refl_equal. % 3.86/4.02 (* end of lemma zenon_L49_ *) % 3.86/4.02 assert (zenon_L50_ : (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e3) (e3)) = (e0)) -> False). % 3.86/4.02 do 0 intro. intros zenon_Hd9 zenon_H22 zenon_Hda. % 3.86/4.02 cut (((op (e0) (e3)) = (e0)) = ((op (e0) (e3)) = (op (e3) (e3)))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_Hd9. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H22. % 3.86/4.02 cut (((e0) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 3.86/4.02 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 3.86/4.02 congruence. % 3.86/4.02 apply zenon_Hc5. apply refl_equal. % 3.86/4.02 apply zenon_Hdb. apply sym_equal. exact zenon_Hda. % 3.86/4.02 (* end of lemma zenon_L50_ *) % 3.86/4.02 assert (zenon_L51_ : (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e3)) = (e3)) -> False). % 3.86/4.02 do 0 intro. intros zenon_Hdc zenon_H5d zenon_H39. % 3.86/4.02 cut (((op (e3) (e2)) = (e3)) = ((op (e3) (e2)) = (op (e3) (e3)))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_Hdc. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H5d. % 3.86/4.02 cut (((e3) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hdd]. % 3.86/4.02 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hb5]. % 3.86/4.02 congruence. % 3.86/4.02 apply zenon_Hb5. apply refl_equal. % 3.86/4.02 apply zenon_Hdd. apply sym_equal. exact zenon_H39. % 3.86/4.02 (* end of lemma zenon_L51_ *) % 3.86/4.02 assert (zenon_L52_ : (((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 (e2) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e2) (e2)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> False). % 3.86/4.02 do 0 intro. intros zenon_Hde zenon_H22 zenon_Hd9 zenon_H8a zenon_H89 zenon_Ha4 zenon_H98 zenon_Hdc zenon_H5d. % 3.86/4.02 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_Hda | zenon_intro zenon_Hdf ]. % 3.86/4.02 apply (zenon_L50_); trivial. % 3.86/4.02 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H68 | zenon_intro zenon_He0 ]. % 3.86/4.02 apply (zenon_L27_); trivial. % 3.86/4.02 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H78 | zenon_intro zenon_H39 ]. % 3.86/4.02 apply (zenon_L35_); trivial. % 3.86/4.02 apply (zenon_L51_); trivial. % 3.86/4.02 (* end of lemma zenon_L52_ *) % 3.86/4.02 assert (zenon_L53_ : (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e3) (e3)) = (e1)) -> False). % 3.86/4.02 do 0 intro. intros zenon_He1 zenon_H58 zenon_H68. % 3.86/4.02 cut (((op (e3) (e1)) = (e1)) = ((op (e3) (e1)) = (op (e3) (e3)))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_He1. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H58. % 3.86/4.02 cut (((e1) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 3.86/4.02 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_He2]. % 3.86/4.02 congruence. % 3.86/4.02 apply zenon_He2. apply refl_equal. % 3.86/4.02 apply zenon_H8b. apply sym_equal. exact zenon_H68. % 3.86/4.02 (* end of lemma zenon_L53_ *) % 3.86/4.02 assert (zenon_L54_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e2) (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))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e1)) -> False). % 3.86/4.02 do 0 intro. intros zenon_He3 zenon_H4a zenon_H29 zenon_H28 zenon_H5d zenon_Hdc zenon_H98 zenon_Ha4 zenon_H89 zenon_Hd9 zenon_H22 zenon_Hde zenon_He1 zenon_H58. % 3.86/4.02 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He4 ]. % 3.86/4.02 apply (zenon_L49_); trivial. % 3.86/4.02 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H27 | zenon_intro zenon_He5 ]. % 3.86/4.02 apply (zenon_L4_); trivial. % 3.86/4.02 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_H8a | zenon_intro zenon_H68 ]. % 3.86/4.02 apply (zenon_L52_); trivial. % 3.86/4.02 apply (zenon_L53_); trivial. % 3.86/4.02 (* end of lemma zenon_L54_ *) % 3.86/4.02 assert (zenon_L55_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e2) (e3)) = (e2))) -> ((op (e2) (e2)) = (e0)) -> ((op (e0) (e2)) = (e1)) -> False). % 3.86/4.02 do 0 intro. intros zenon_H8d zenon_H53 zenon_He1 zenon_Hde zenon_Hd9 zenon_H89 zenon_Hdc zenon_H28 zenon_H29 zenon_H4a zenon_He3 zenon_H5d zenon_H5c zenon_H92 zenon_H61 zenon_H22 zenon_H66 zenon_H91 zenon_H98 zenon_Ha4. % 3.86/4.02 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H54 | zenon_intro zenon_H8e ]. % 3.86/4.02 apply (zenon_L16_); trivial. % 3.86/4.02 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H58 | zenon_intro zenon_H8f ]. % 3.86/4.02 apply (zenon_L54_); trivial. % 3.86/4.02 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H5e | zenon_intro zenon_H68 ]. % 3.86/4.02 apply (zenon_L19_); trivial. % 3.86/4.02 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H60 | zenon_intro zenon_H95 ]. % 3.86/4.02 apply (zenon_L20_); trivial. % 3.86/4.02 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H69 | zenon_intro zenon_H96 ]. % 3.86/4.02 apply (zenon_L23_); trivial. % 3.86/4.02 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H32 | zenon_intro zenon_H78 ]. % 3.86/4.02 exact (zenon_H91 zenon_H32). % 3.86/4.02 apply (zenon_L35_); trivial. % 3.86/4.02 (* end of lemma zenon_L55_ *) % 3.86/4.02 assert (zenon_L56_ : (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (e1)) = (e1)) -> False). % 3.86/4.02 do 0 intro. intros zenon_He6 zenon_H28 zenon_H1f. % 3.86/4.02 cut (((op (e1) (e0)) = (e1)) = ((op (e1) (e0)) = (op (e1) (e1)))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_He6. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H28. % 3.86/4.02 cut (((e1) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_He7]. % 3.86/4.02 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H44]. % 3.86/4.02 congruence. % 3.86/4.02 apply zenon_H44. apply refl_equal. % 3.86/4.02 apply zenon_He7. apply sym_equal. exact zenon_H1f. % 3.86/4.02 (* end of lemma zenon_L56_ *) % 3.86/4.02 assert (zenon_L57_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (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 (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 3.86/4.02 do 0 intro. intros zenon_He8 zenon_H42 zenon_H9b zenon_Hbc zenon_H5c zenon_H9e zenon_H20 zenon_H89 zenon_H56 zenon_H53 zenon_H28 zenon_H8d zenon_H92 zenon_H61 zenon_H91 zenon_H50 zenon_H90 zenon_He9 zenon_Hd1 zenon_H5d zenon_Hce zenon_H31 zenon_Ha3 zenon_H97 zenon_H48 zenon_Hd4 zenon_H22 zenon_H4a. % 3.86/4.02 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hea ]. % 3.86/4.02 apply (zenon_L11_); trivial. % 3.86/4.02 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H57 | zenon_intro zenon_Heb ]. % 3.86/4.02 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H66 | zenon_intro zenon_Hec ]. % 3.86/4.02 apply (zenon_L32_); trivial. % 3.86/4.02 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hed ]. % 3.86/4.02 apply (zenon_L43_); trivial. % 3.86/4.02 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hca ]. % 3.86/4.02 apply (zenon_L40_); trivial. % 3.86/4.02 apply (zenon_L44_); trivial. % 3.86/4.02 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Ha4 | zenon_intro zenon_Hd7 ]. % 3.86/4.02 apply (zenon_L48_); trivial. % 3.86/4.02 apply (zenon_L49_); trivial. % 3.86/4.02 (* end of lemma zenon_L57_ *) % 3.86/4.02 assert (zenon_L58_ : (((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) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 3.86/4.02 do 0 intro. intros zenon_Hee zenon_Hd4 zenon_H97 zenon_Ha3 zenon_Hce zenon_Hd1 zenon_He9 zenon_H90 zenon_H50 zenon_H91 zenon_H92 zenon_H8d zenon_H53 zenon_H56 zenon_H20 zenon_H9e zenon_H5c zenon_Hbc zenon_H9b zenon_H42 zenon_He8 zenon_H31 zenon_H61 zenon_H58 zenon_He1 zenon_Hde zenon_Hd9 zenon_H89 zenon_Ha4 zenon_Hdc zenon_H5d zenon_H28 zenon_H29 zenon_H4a zenon_He3 zenon_Hc2 zenon_H22. % 3.86/4.02 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H48 | zenon_intro zenon_Hef ]. % 3.86/4.02 apply (zenon_L57_); trivial. % 3.86/4.02 apply (zenon_or_s _ _ zenon_Hef); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hf0 ]. % 3.86/4.02 apply (zenon_L33_); trivial. % 3.86/4.02 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H98 | zenon_intro zenon_Hc3 ]. % 3.86/4.02 apply (zenon_L54_); trivial. % 3.86/4.02 apply (zenon_L42_); trivial. % 3.86/4.02 (* end of lemma zenon_L58_ *) % 3.86/4.02 assert (zenon_L59_ : (((op (e2) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3)))) -> (~((op (e2) (e3)) = (e2))) -> False). % 3.86/4.02 do 0 intro. intros zenon_H35 zenon_H91. % 3.86/4.02 apply (zenon_and_s _ _ zenon_H35). zenon_intro zenon_H32. zenon_intro zenon_H36. % 3.86/4.02 exact (zenon_H91 zenon_H32). % 3.86/4.02 (* end of lemma zenon_L59_ *) % 3.86/4.02 assert (zenon_L60_ : (((op (e1) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3)))) -> (~((op (e1) (e3)) = (e1))) -> False). % 3.86/4.02 do 0 intro. intros zenon_H2e zenon_Hf1. % 3.86/4.02 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H27. zenon_intro zenon_H2f. % 3.86/4.02 exact (zenon_Hf1 zenon_H27). % 3.86/4.02 (* end of lemma zenon_L60_ *) % 3.86/4.02 assert (zenon_L61_ : (~((e0) = (e1))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (e0)) = (e0)) -> False). % 3.86/4.02 do 0 intro. intros zenon_H4a zenon_H28 zenon_Hf2. % 3.86/4.02 cut (((op (e1) (e0)) = (e1)) = ((e0) = (e1))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_H4a. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H28. % 3.86/4.02 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 3.86/4.02 cut (((op (e1) (e0)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hf3]. % 3.86/4.02 congruence. % 3.86/4.02 exact (zenon_Hf3 zenon_Hf2). % 3.86/4.02 apply zenon_H4c. apply refl_equal. % 3.86/4.02 (* end of lemma zenon_L61_ *) % 3.86/4.02 assert (zenon_L62_ : ((op (e2) (e0)) = (e0)) -> ((op (e2) (e0)) = (e3)) -> (~((e0) = (e3))) -> False). % 3.86/4.02 do 0 intro. intros zenon_H48 zenon_Hf4 zenon_H9b. % 3.86/4.02 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H5b ]. % 3.86/4.02 cut (((e3) = (e3)) = ((e0) = (e3))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_H9b. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_Hc7. % 3.86/4.02 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H5b]. % 3.86/4.02 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 3.86/4.02 congruence. % 3.86/4.02 cut (((op (e2) (e0)) = (e0)) = ((e3) = (e0))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_Hcb. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H48. % 3.86/4.02 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H47]. % 3.86/4.02 cut (((op (e2) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 3.86/4.02 congruence. % 3.86/4.02 exact (zenon_Hf5 zenon_Hf4). % 3.86/4.02 apply zenon_H47. apply refl_equal. % 3.86/4.02 apply zenon_H5b. apply refl_equal. % 3.86/4.02 apply zenon_H5b. apply refl_equal. % 3.86/4.02 (* end of lemma zenon_L62_ *) % 3.86/4.02 assert (zenon_L63_ : ((op (e3) (e1)) = (e3)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> False). % 3.86/4.02 do 0 intro. intros zenon_Hf6 zenon_Hf7 zenon_Hf8. % 3.86/4.02 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_Hf9 | zenon_intro zenon_He2 ]. % 3.86/4.02 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e2) (e1)) = (op (e3) (e1)))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_Hf8. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_Hf9. % 3.86/4.02 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_He2]. % 3.86/4.02 cut (((op (e3) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hfa]. % 3.86/4.02 congruence. % 3.86/4.02 cut (((op (e3) (e1)) = (e3)) = ((op (e3) (e1)) = (op (e2) (e1)))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_Hfa. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_Hf6. % 3.86/4.02 cut (((e3) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hfb]. % 3.86/4.02 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_He2]. % 3.86/4.02 congruence. % 3.86/4.02 apply zenon_He2. apply refl_equal. % 3.86/4.02 apply zenon_Hfb. apply sym_equal. exact zenon_Hf7. % 3.86/4.02 apply zenon_He2. apply refl_equal. % 3.86/4.02 apply zenon_He2. apply refl_equal. % 3.86/4.02 (* end of lemma zenon_L63_ *) % 3.86/4.02 assert (zenon_L64_ : ((op (e0) (e2)) = (e0)) -> ((op (e0) (e2)) = (e3)) -> (~((e0) = (e3))) -> False). % 3.86/4.02 do 0 intro. intros zenon_H21 zenon_Hbb zenon_H9b. % 3.86/4.02 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H5b ]. % 3.86/4.02 cut (((e3) = (e3)) = ((e0) = (e3))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_H9b. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_Hc7. % 3.86/4.02 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H5b]. % 3.86/4.02 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 3.86/4.02 congruence. % 3.86/4.02 cut (((op (e0) (e2)) = (e0)) = ((e3) = (e0))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_Hcb. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H21. % 3.86/4.02 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H47]. % 3.86/4.02 cut (((op (e0) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hfc]. % 3.86/4.02 congruence. % 3.86/4.02 exact (zenon_Hfc zenon_Hbb). % 3.86/4.02 apply zenon_H47. apply refl_equal. % 3.86/4.02 apply zenon_H5b. apply refl_equal. % 3.86/4.02 apply zenon_H5b. apply refl_equal. % 3.86/4.02 (* end of lemma zenon_L64_ *) % 3.86/4.02 assert (zenon_L65_ : (~((op (op (e0) (e0)) (op (e0) (e0))) = (op (e2) (e2)))) -> ((op (e0) (e0)) = (e2)) -> False). % 3.86/4.02 do 0 intro. intros zenon_Hfd zenon_Hfe. % 3.86/4.02 cut (((op (e0) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hff]. % 3.86/4.02 cut (((op (e0) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hff]. % 3.86/4.02 congruence. % 3.86/4.02 exact (zenon_Hff zenon_Hfe). % 3.86/4.02 exact (zenon_Hff zenon_Hfe). % 3.86/4.02 (* end of lemma zenon_L65_ *) % 3.86/4.02 assert (zenon_L66_ : ((op (e2) (e2)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (~((e1) = (op (op (e0) (e0)) (op (e0) (e0))))) -> False). % 3.86/4.02 do 0 intro. intros zenon_H7a zenon_Hfe zenon_H6b. % 3.86/4.02 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H6c | zenon_intro zenon_H6d ]. % 3.86/4.02 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((e1) = (op (op (e0) (e0)) (op (e0) (e0))))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_H6b. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H6c. % 3.86/4.02 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 3.86/4.02 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H6e]. % 3.86/4.02 congruence. % 3.86/4.02 cut (((op (e2) (e2)) = (e1)) = ((op (op (e0) (e0)) (op (e0) (e0))) = (e1))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_H6e. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H7a. % 3.86/4.02 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 3.86/4.02 cut (((op (e2) (e2)) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H100]. % 3.86/4.02 congruence. % 3.86/4.02 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H6c | zenon_intro zenon_H6d ]. % 3.86/4.02 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((op (e2) (e2)) = (op (op (e0) (e0)) (op (e0) (e0))))). % 3.86/4.02 intro zenon_D_pnotp. % 3.86/4.02 apply zenon_H100. % 3.86/4.02 rewrite <- zenon_D_pnotp. % 3.86/4.02 exact zenon_H6c. % 3.86/4.02 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 3.86/4.02 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hfd]. % 3.86/4.03 congruence. % 3.86/4.03 apply (zenon_L65_); trivial. % 3.86/4.03 apply zenon_H6d. apply refl_equal. % 3.86/4.03 apply zenon_H6d. apply refl_equal. % 3.86/4.03 apply zenon_H4c. apply refl_equal. % 3.86/4.03 apply zenon_H6d. apply refl_equal. % 3.86/4.03 apply zenon_H6d. apply refl_equal. % 3.86/4.03 (* end of lemma zenon_L66_ *) % 3.86/4.03 assert (zenon_L67_ : ((op (e2) (e2)) = (e1)) -> ((op (e1) (e2)) = (e3)) -> ((op (e0) (e0)) = (e2)) -> False). % 3.86/4.03 do 0 intro. intros zenon_H7a zenon_Hb2 zenon_Hfe. % 3.86/4.03 apply (zenon_notand_s _ _ ax16); [ zenon_intro zenon_H6b | zenon_intro zenon_H101 ]. % 3.86/4.03 apply (zenon_L66_); trivial. % 3.86/4.03 apply (zenon_notand_s _ _ zenon_H101); [ zenon_intro zenon_H103 | zenon_intro zenon_H102 ]. % 3.86/4.03 elim (classic ((op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))))); [ zenon_intro zenon_H72 | zenon_intro zenon_H73 ]. % 3.86/4.03 cut (((op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) = ((e3) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H103. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H72. % 3.86/4.03 cut (((op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 3.86/4.03 cut (((op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H104]. % 3.86/4.03 congruence. % 3.86/4.03 cut (((op (e1) (e2)) = (e3)) = ((op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))) = (e3))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H104. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_Hb2. % 3.86/4.03 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H5b]. % 3.86/4.03 cut (((op (e1) (e2)) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H105]. % 3.86/4.03 congruence. % 3.86/4.03 elim (classic ((op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))))); [ zenon_intro zenon_H72 | zenon_intro zenon_H73 ]. % 3.86/4.03 cut (((op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) = ((op (e1) (e2)) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H105. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H72. % 3.86/4.03 cut (((op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 3.86/4.03 cut (((op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H106]. % 3.86/4.03 congruence. % 3.86/4.03 cut (((op (e0) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hff]. % 3.86/4.03 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H6e]. % 3.86/4.03 congruence. % 3.86/4.03 cut (((op (e2) (e2)) = (e1)) = ((op (op (e0) (e0)) (op (e0) (e0))) = (e1))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H6e. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H7a. % 3.86/4.03 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 3.86/4.03 cut (((op (e2) (e2)) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H100]. % 3.86/4.03 congruence. % 3.86/4.03 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H6c | zenon_intro zenon_H6d ]. % 3.86/4.03 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((op (e2) (e2)) = (op (op (e0) (e0)) (op (e0) (e0))))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H100. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H6c. % 3.86/4.03 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 3.86/4.03 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hfd]. % 3.86/4.03 congruence. % 3.86/4.03 apply (zenon_L65_); trivial. % 3.86/4.03 apply zenon_H6d. apply refl_equal. % 3.86/4.03 apply zenon_H6d. apply refl_equal. % 3.86/4.03 apply zenon_H4c. apply refl_equal. % 3.86/4.03 exact (zenon_Hff zenon_Hfe). % 3.86/4.03 apply zenon_H73. apply refl_equal. % 3.86/4.03 apply zenon_H73. apply refl_equal. % 3.86/4.03 apply zenon_H5b. apply refl_equal. % 3.86/4.03 apply zenon_H73. apply refl_equal. % 3.86/4.03 apply zenon_H73. apply refl_equal. % 3.86/4.03 apply zenon_H102. apply sym_equal. exact zenon_Hfe. % 3.86/4.03 (* end of lemma zenon_L67_ *) % 3.86/4.03 assert (zenon_L68_ : ((op (e2) (e3)) = (e2)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> False). % 3.86/4.03 do 0 intro. intros zenon_H32 zenon_H40 zenon_H107. % 3.86/4.03 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H108 | zenon_intro zenon_H8c ]. % 3.86/4.03 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e2) (e2)) = (op (e2) (e3)))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H107. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H108. % 3.86/4.03 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H8c]. % 3.86/4.03 cut (((op (e2) (e3)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H109]. % 3.86/4.03 congruence. % 3.86/4.03 cut (((op (e2) (e3)) = (e2)) = ((op (e2) (e3)) = (op (e2) (e2)))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H109. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H32. % 3.86/4.03 cut (((e2) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hcf]. % 3.86/4.03 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H8c]. % 3.86/4.03 congruence. % 3.86/4.03 apply zenon_H8c. apply refl_equal. % 3.86/4.03 apply zenon_Hcf. apply sym_equal. exact zenon_H40. % 3.86/4.03 apply zenon_H8c. apply refl_equal. % 3.86/4.03 apply zenon_H8c. apply refl_equal. % 3.86/4.03 (* end of lemma zenon_L68_ *) % 3.86/4.03 assert (zenon_L69_ : (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e0)) -> ((op (e3) (e3)) = (e0)) -> False). % 3.86/4.03 do 0 intro. intros zenon_H10a zenon_H10b zenon_Hda. % 3.86/4.03 cut (((op (e1) (e3)) = (e0)) = ((op (e1) (e3)) = (op (e3) (e3)))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H10a. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H10b. % 3.86/4.03 cut (((e0) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 3.86/4.03 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 3.86/4.03 congruence. % 3.86/4.03 apply zenon_H2b. apply refl_equal. % 3.86/4.03 apply zenon_Hdb. apply sym_equal. exact zenon_Hda. % 3.86/4.03 (* end of lemma zenon_L69_ *) % 3.86/4.03 assert (zenon_L70_ : (~((op (op (e2) (e2)) (op (e2) (e2))) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e3)) -> False). % 3.86/4.03 do 0 intro. intros zenon_H10c zenon_Hd0. % 3.86/4.03 cut (((op (e2) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H10d]. % 3.86/4.03 cut (((op (e2) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H10d]. % 3.86/4.03 congruence. % 3.86/4.03 exact (zenon_H10d zenon_Hd0). % 3.86/4.03 exact (zenon_H10d zenon_Hd0). % 3.86/4.03 (* end of lemma zenon_L70_ *) % 3.86/4.03 assert (zenon_L71_ : ((op (e3) (e3)) = (e1)) -> ((op (e2) (e2)) = (e3)) -> (~((e1) = (op (op (e2) (e2)) (op (e2) (e2))))) -> False). % 3.86/4.03 do 0 intro. intros zenon_H68 zenon_Hd0 zenon_H10e. % 3.86/4.03 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H10f | zenon_intro zenon_H110 ]. % 3.86/4.03 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((e1) = (op (op (e2) (e2)) (op (e2) (e2))))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H10e. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H10f. % 3.86/4.03 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H110]. % 3.86/4.03 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H111]. % 3.86/4.03 congruence. % 3.86/4.03 cut (((op (e3) (e3)) = (e1)) = ((op (op (e2) (e2)) (op (e2) (e2))) = (e1))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H111. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H68. % 3.86/4.03 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 3.86/4.03 cut (((op (e3) (e3)) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H112]. % 3.86/4.03 congruence. % 3.86/4.03 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H10f | zenon_intro zenon_H110 ]. % 3.86/4.03 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((op (e3) (e3)) = (op (op (e2) (e2)) (op (e2) (e2))))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H112. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H10f. % 3.86/4.03 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H110]. % 3.86/4.03 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H10c]. % 3.86/4.03 congruence. % 3.86/4.03 apply (zenon_L70_); trivial. % 3.86/4.03 apply zenon_H110. apply refl_equal. % 3.86/4.03 apply zenon_H110. apply refl_equal. % 3.86/4.03 apply zenon_H4c. apply refl_equal. % 3.86/4.03 apply zenon_H110. apply refl_equal. % 3.86/4.03 apply zenon_H110. apply refl_equal. % 3.86/4.03 (* end of lemma zenon_L71_ *) % 3.86/4.03 assert (zenon_L72_ : ((op (e3) (e3)) = (e1)) -> ((op (e1) (e3)) = (e0)) -> ((op (e2) (e2)) = (e3)) -> False). % 3.86/4.03 do 0 intro. intros zenon_H68 zenon_H10b zenon_Hd0. % 3.86/4.03 apply (zenon_notand_s _ _ ax12); [ zenon_intro zenon_H10e | zenon_intro zenon_H113 ]. % 3.86/4.03 apply (zenon_L71_); trivial. % 3.86/4.03 apply (zenon_notand_s _ _ zenon_H113); [ zenon_intro zenon_H114 | zenon_intro zenon_Hd3 ]. % 3.86/4.03 elim (classic ((op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))))); [ zenon_intro zenon_H115 | zenon_intro zenon_H116 ]. % 3.86/4.03 cut (((op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) = ((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H114. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H115. % 3.86/4.03 cut (((op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H116]. % 3.86/4.03 cut (((op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H117]. % 3.86/4.03 congruence. % 3.86/4.03 cut (((op (e1) (e3)) = (e0)) = ((op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))) = (e0))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H117. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H10b. % 3.86/4.03 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H47]. % 3.86/4.03 cut (((op (e1) (e3)) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H118]. % 3.86/4.03 congruence. % 3.86/4.03 elim (classic ((op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))))); [ zenon_intro zenon_H115 | zenon_intro zenon_H116 ]. % 3.86/4.03 cut (((op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) = ((op (e1) (e3)) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H118. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H115. % 3.86/4.03 cut (((op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H116]. % 3.86/4.03 cut (((op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H119]. % 3.86/4.03 congruence. % 3.86/4.03 cut (((op (e2) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H10d]. % 3.86/4.03 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H111]. % 3.86/4.03 congruence. % 3.86/4.03 cut (((op (e3) (e3)) = (e1)) = ((op (op (e2) (e2)) (op (e2) (e2))) = (e1))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H111. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H68. % 3.86/4.03 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 3.86/4.03 cut (((op (e3) (e3)) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H112]. % 3.86/4.03 congruence. % 3.86/4.03 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H10f | zenon_intro zenon_H110 ]. % 3.86/4.03 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((op (e3) (e3)) = (op (op (e2) (e2)) (op (e2) (e2))))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H112. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H10f. % 3.86/4.03 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H110]. % 3.86/4.03 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H10c]. % 3.86/4.03 congruence. % 3.86/4.03 apply (zenon_L70_); trivial. % 3.86/4.03 apply zenon_H110. apply refl_equal. % 3.86/4.03 apply zenon_H110. apply refl_equal. % 3.86/4.03 apply zenon_H4c. apply refl_equal. % 3.86/4.03 exact (zenon_H10d zenon_Hd0). % 3.86/4.03 apply zenon_H116. apply refl_equal. % 3.86/4.03 apply zenon_H116. apply refl_equal. % 3.86/4.03 apply zenon_H47. apply refl_equal. % 3.86/4.03 apply zenon_H116. apply refl_equal. % 3.86/4.03 apply zenon_H116. apply refl_equal. % 3.86/4.03 apply zenon_Hd3. apply sym_equal. exact zenon_Hd0. % 3.86/4.03 (* end of lemma zenon_L72_ *) % 3.86/4.03 assert (zenon_L73_ : (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e3)) = (e2)) -> False). % 3.86/4.03 do 0 intro. intros zenon_H89 zenon_H32 zenon_H78. % 3.86/4.03 cut (((op (e2) (e3)) = (e2)) = ((op (e2) (e3)) = (op (e3) (e3)))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H89. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H32. % 3.86/4.03 cut (((e2) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 3.86/4.03 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H8c]. % 3.86/4.03 congruence. % 3.86/4.03 apply zenon_H8c. apply refl_equal. % 3.86/4.03 apply zenon_H82. apply sym_equal. exact zenon_H78. % 3.86/4.03 (* end of lemma zenon_L73_ *) % 3.86/4.03 assert (zenon_L74_ : (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e3)) = (e3)) -> False). % 3.86/4.03 do 0 intro. intros zenon_He1 zenon_Hf6 zenon_H39. % 3.86/4.03 cut (((op (e3) (e1)) = (e3)) = ((op (e3) (e1)) = (op (e3) (e3)))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_He1. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_Hf6. % 3.86/4.03 cut (((e3) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hdd]. % 3.86/4.03 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_He2]. % 3.86/4.03 congruence. % 3.86/4.03 apply zenon_He2. apply refl_equal. % 3.86/4.03 apply zenon_Hdd. apply sym_equal. exact zenon_H39. % 3.86/4.03 (* end of lemma zenon_L74_ *) % 3.86/4.03 assert (zenon_L75_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e1) (e3)) = (e0)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> False). % 3.86/4.03 do 0 intro. intros zenon_Hde zenon_H10a zenon_Hd0 zenon_H10b zenon_H32 zenon_H89 zenon_He1 zenon_Hf6. % 3.86/4.03 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_Hda | zenon_intro zenon_Hdf ]. % 3.86/4.03 apply (zenon_L69_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H68 | zenon_intro zenon_He0 ]. % 3.86/4.03 apply (zenon_L72_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H78 | zenon_intro zenon_H39 ]. % 3.86/4.03 apply (zenon_L73_); trivial. % 3.86/4.03 apply (zenon_L74_); trivial. % 3.86/4.03 (* end of lemma zenon_L75_ *) % 3.86/4.03 assert (zenon_L76_ : (((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 (e0) (e0)) = (e2)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e0)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> False). % 3.86/4.03 do 0 intro. intros zenon_Hd4 zenon_H48 zenon_H97 zenon_Hfe zenon_Hb2 zenon_H107 zenon_Hde zenon_H10a zenon_H10b zenon_H32 zenon_H89 zenon_He1 zenon_Hf6. % 3.86/4.03 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H98 | zenon_intro zenon_Hd5 ]. % 3.86/4.03 apply (zenon_L30_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H7a | zenon_intro zenon_Hd6 ]. % 3.86/4.03 apply (zenon_L67_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H40 | zenon_intro zenon_Hd0 ]. % 3.86/4.03 apply (zenon_L68_); trivial. % 3.86/4.03 apply (zenon_L75_); trivial. % 3.86/4.03 (* end of lemma zenon_L76_ *) % 3.86/4.03 assert (zenon_L77_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e0)) = (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) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> False). % 3.86/4.03 do 0 intro. intros zenon_H11a zenon_H9b zenon_H21 zenon_H107 zenon_Hfe zenon_H97 zenon_H48 zenon_Hd4 zenon_Hf6 zenon_He1 zenon_H89 zenon_H32 zenon_H10b zenon_H10a zenon_Hde zenon_H36. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H11a); [ zenon_intro zenon_Hbb | zenon_intro zenon_H11b ]. % 3.86/4.03 apply (zenon_L64_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_Hb2 | zenon_intro zenon_H11c ]. % 3.86/4.03 apply (zenon_L76_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H5d ]. % 3.86/4.03 apply (zenon_L75_); trivial. % 3.86/4.03 exact (zenon_H36 zenon_H5d). % 3.86/4.03 (* end of lemma zenon_L77_ *) % 3.86/4.03 assert (zenon_L78_ : (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> ((op (e2) (e3)) = (e0)) -> False). % 3.86/4.03 do 0 intro. intros zenon_H61 zenon_H32 zenon_Hc3. % 3.86/4.03 cut (((op (e2) (e3)) = (e2)) = ((e0) = (e2))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H61. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H32. % 3.86/4.03 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 3.86/4.03 cut (((op (e2) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H11d]. % 3.86/4.03 congruence. % 3.86/4.03 exact (zenon_H11d zenon_Hc3). % 3.86/4.03 apply zenon_H4f. apply refl_equal. % 3.86/4.03 (* end of lemma zenon_L78_ *) % 3.86/4.03 assert (zenon_L79_ : ((op (e3) (e3)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> ((op (e2) (e2)) = (e3)) -> False). % 3.86/4.03 do 0 intro. intros zenon_Hda zenon_Hd7 zenon_Hd0. % 3.86/4.03 apply (zenon_notand_s _ _ ax6); [ zenon_intro zenon_H11f | zenon_intro zenon_H11e ]. % 3.86/4.03 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H10f | zenon_intro zenon_H110 ]. % 3.86/4.03 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((e0) = (op (op (e2) (e2)) (op (e2) (e2))))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H11f. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H10f. % 3.86/4.03 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H110]. % 3.86/4.03 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H120]. % 3.86/4.03 congruence. % 3.86/4.03 cut (((op (e3) (e3)) = (e0)) = ((op (op (e2) (e2)) (op (e2) (e2))) = (e0))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H120. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_Hda. % 3.86/4.03 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H47]. % 3.86/4.03 cut (((op (e3) (e3)) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H112]. % 3.86/4.03 congruence. % 3.86/4.03 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H10f | zenon_intro zenon_H110 ]. % 3.86/4.03 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((op (e3) (e3)) = (op (op (e2) (e2)) (op (e2) (e2))))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H112. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H10f. % 3.86/4.03 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H110]. % 3.86/4.03 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H10c]. % 3.86/4.03 congruence. % 3.86/4.03 apply (zenon_L70_); trivial. % 3.86/4.03 apply zenon_H110. apply refl_equal. % 3.86/4.03 apply zenon_H110. apply refl_equal. % 3.86/4.03 apply zenon_H47. apply refl_equal. % 3.86/4.03 apply zenon_H110. apply refl_equal. % 3.86/4.03 apply zenon_H110. apply refl_equal. % 3.86/4.03 apply (zenon_notand_s _ _ zenon_H11e); [ zenon_intro zenon_H121 | zenon_intro zenon_Hd3 ]. % 3.86/4.03 elim (classic ((op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))))); [ zenon_intro zenon_H115 | zenon_intro zenon_H116 ]. % 3.86/4.03 cut (((op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) = ((e1) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H121. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H115. % 3.86/4.03 cut (((op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H116]. % 3.86/4.03 cut (((op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H122]. % 3.86/4.03 congruence. % 3.86/4.03 cut (((op (e0) (e3)) = (e1)) = ((op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))) = (e1))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H122. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_Hd7. % 3.86/4.03 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 3.86/4.03 cut (((op (e0) (e3)) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H123]. % 3.86/4.03 congruence. % 3.86/4.03 elim (classic ((op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))))); [ zenon_intro zenon_H115 | zenon_intro zenon_H116 ]. % 3.86/4.03 cut (((op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) = ((op (e0) (e3)) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H123. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H115. % 3.86/4.03 cut (((op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H116]. % 3.86/4.03 cut (((op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H124]. % 3.86/4.03 congruence. % 3.86/4.03 cut (((op (e2) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H10d]. % 3.86/4.03 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H120]. % 3.86/4.03 congruence. % 3.86/4.03 cut (((op (e3) (e3)) = (e0)) = ((op (op (e2) (e2)) (op (e2) (e2))) = (e0))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H120. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_Hda. % 3.86/4.03 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H47]. % 3.86/4.03 cut (((op (e3) (e3)) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H112]. % 3.86/4.03 congruence. % 3.86/4.03 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H10f | zenon_intro zenon_H110 ]. % 3.86/4.03 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((op (e3) (e3)) = (op (op (e2) (e2)) (op (e2) (e2))))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H112. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H10f. % 3.86/4.03 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H110]. % 3.86/4.03 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H10c]. % 3.86/4.03 congruence. % 3.86/4.03 apply (zenon_L70_); trivial. % 3.86/4.03 apply zenon_H110. apply refl_equal. % 3.86/4.03 apply zenon_H110. apply refl_equal. % 3.86/4.03 apply zenon_H47. apply refl_equal. % 3.86/4.03 exact (zenon_H10d zenon_Hd0). % 3.86/4.03 apply zenon_H116. apply refl_equal. % 3.86/4.03 apply zenon_H116. apply refl_equal. % 3.86/4.03 apply zenon_H4c. apply refl_equal. % 3.86/4.03 apply zenon_H116. apply refl_equal. % 3.86/4.03 apply zenon_H116. apply refl_equal. % 3.86/4.03 apply zenon_Hd3. apply sym_equal. exact zenon_Hd0. % 3.86/4.03 (* end of lemma zenon_L79_ *) % 3.86/4.03 assert (zenon_L80_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> (((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 (e0) (e0)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e1)) -> ((op (e2) (e2)) = (e3)) -> False). % 3.86/4.03 do 0 intro. intros zenon_H125 zenon_H4a zenon_H36 zenon_Hde zenon_H10a zenon_H89 zenon_He1 zenon_Hf6 zenon_Hd4 zenon_H48 zenon_H97 zenon_Hfe zenon_H107 zenon_H21 zenon_H9b zenon_H11a zenon_H32 zenon_H61 zenon_Hd7 zenon_Hd0. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H22 | zenon_intro zenon_H126 ]. % 3.86/4.03 apply (zenon_L49_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H10b | zenon_intro zenon_H127 ]. % 3.86/4.03 apply (zenon_L77_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hda ]. % 3.86/4.03 apply (zenon_L78_); trivial. % 3.86/4.03 apply (zenon_L79_); trivial. % 3.86/4.03 (* end of lemma zenon_L80_ *) % 3.86/4.03 assert (zenon_L81_ : ((op (e2) (e3)) = (e2)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 3.86/4.03 do 0 intro. intros zenon_H32 zenon_H69 zenon_H128. % 3.86/4.03 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H108 | zenon_intro zenon_H8c ]. % 3.86/4.03 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e1) (e3)) = (op (e2) (e3)))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H128. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H108. % 3.86/4.03 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H8c]. % 3.86/4.03 cut (((op (e2) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H129]. % 3.86/4.03 congruence. % 3.86/4.03 cut (((op (e2) (e3)) = (e2)) = ((op (e2) (e3)) = (op (e1) (e3)))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H129. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H32. % 3.86/4.03 cut (((e2) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12a]. % 3.86/4.03 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H8c]. % 3.86/4.03 congruence. % 3.86/4.03 apply zenon_H8c. apply refl_equal. % 3.86/4.03 apply zenon_H12a. apply sym_equal. exact zenon_H69. % 3.86/4.03 apply zenon_H8c. apply refl_equal. % 3.86/4.03 apply zenon_H8c. apply refl_equal. % 3.86/4.03 (* end of lemma zenon_L81_ *) % 3.86/4.03 assert (zenon_L82_ : (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> False). % 3.86/4.03 do 0 intro. intros zenon_H128 zenon_H12b zenon_H12c. % 3.86/4.03 cut (((op (e1) (e3)) = (e3)) = ((op (e1) (e3)) = (op (e2) (e3)))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H128. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H12b. % 3.86/4.03 cut (((e3) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12d]. % 3.86/4.03 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 3.86/4.03 congruence. % 3.86/4.03 apply zenon_H2b. apply refl_equal. % 3.86/4.03 apply zenon_H12d. apply sym_equal. exact zenon_H12c. % 3.86/4.03 (* end of lemma zenon_L82_ *) % 3.86/4.03 assert (zenon_L83_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 3.86/4.03 do 0 intro. intros zenon_H12e zenon_Hda zenon_H10a zenon_Hf1 zenon_H32 zenon_H128 zenon_H12c. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H10b | zenon_intro zenon_H12f ]. % 3.86/4.03 apply (zenon_L69_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H27 | zenon_intro zenon_H130 ]. % 3.86/4.03 exact (zenon_Hf1 zenon_H27). % 3.86/4.03 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H69 | zenon_intro zenon_H12b ]. % 3.86/4.03 apply (zenon_L81_); trivial. % 3.86/4.03 apply (zenon_L82_); trivial. % 3.86/4.03 (* end of lemma zenon_L83_ *) % 3.86/4.03 assert (zenon_L84_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e3)) -> ((op (e0) (e0)) = (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))))) -> (~((e0) = (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) (e3)) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 3.86/4.03 do 0 intro. intros zenon_H125 zenon_H21 zenon_H20 zenon_Hf6 zenon_He1 zenon_H89 zenon_Hde zenon_H107 zenon_Hb2 zenon_Hfe zenon_H97 zenon_H48 zenon_Hd4 zenon_H61 zenon_H12e zenon_H10a zenon_Hf1 zenon_H32 zenon_H128 zenon_H12c. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H22 | zenon_intro zenon_H126 ]. % 3.86/4.03 apply (zenon_L2_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H10b | zenon_intro zenon_H127 ]. % 3.86/4.03 apply (zenon_L76_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hda ]. % 3.86/4.03 apply (zenon_L78_); trivial. % 3.86/4.03 apply (zenon_L83_); trivial. % 3.86/4.03 (* end of lemma zenon_L84_ *) % 3.86/4.03 assert (zenon_L85_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e3)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (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) (e3)) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 3.86/4.03 do 0 intro. intros zenon_H125 zenon_H21 zenon_H20 zenon_Hf6 zenon_He1 zenon_H89 zenon_Hd0 zenon_Hde zenon_H61 zenon_H12e zenon_H10a zenon_Hf1 zenon_H32 zenon_H128 zenon_H12c. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H22 | zenon_intro zenon_H126 ]. % 3.86/4.03 apply (zenon_L2_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H10b | zenon_intro zenon_H127 ]. % 3.86/4.03 apply (zenon_L75_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hda ]. % 3.86/4.03 apply (zenon_L78_); trivial. % 3.86/4.03 apply (zenon_L83_); trivial. % 3.86/4.03 (* end of lemma zenon_L85_ *) % 3.86/4.03 assert (zenon_L86_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (((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 (e0) (e0)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (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) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (e3))) -> False). % 3.86/4.03 do 0 intro. intros zenon_H11a zenon_H9b zenon_Hd4 zenon_H48 zenon_H97 zenon_Hfe zenon_H107 zenon_H12c zenon_H128 zenon_H32 zenon_Hf1 zenon_H10a zenon_H12e zenon_H61 zenon_Hde zenon_H89 zenon_He1 zenon_Hf6 zenon_H20 zenon_H21 zenon_H125 zenon_H36. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H11a); [ zenon_intro zenon_Hbb | zenon_intro zenon_H11b ]. % 3.86/4.03 apply (zenon_L64_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_Hb2 | zenon_intro zenon_H11c ]. % 3.86/4.03 apply (zenon_L84_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H5d ]. % 3.86/4.03 apply (zenon_L85_); trivial. % 3.86/4.03 exact (zenon_H36 zenon_H5d). % 3.86/4.03 (* end of lemma zenon_L86_ *) % 3.86/4.03 assert (zenon_L87_ : ((op (e2) (e0)) = (e0)) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> False). % 3.86/4.03 do 0 intro. intros zenon_H48 zenon_Hf2 zenon_H131. % 3.86/4.03 elim (classic ((op (e2) (e0)) = (op (e2) (e0)))); [ zenon_intro zenon_H132 | zenon_intro zenon_H9a ]. % 3.86/4.03 cut (((op (e2) (e0)) = (op (e2) (e0))) = ((op (e1) (e0)) = (op (e2) (e0)))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H131. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H132. % 3.86/4.03 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 3.86/4.03 cut (((op (e2) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H133]. % 3.86/4.03 congruence. % 3.86/4.03 cut (((op (e2) (e0)) = (e0)) = ((op (e2) (e0)) = (op (e1) (e0)))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H133. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H48. % 3.86/4.03 cut (((e0) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H134]. % 3.86/4.03 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 3.86/4.03 congruence. % 3.86/4.03 apply zenon_H9a. apply refl_equal. % 3.86/4.03 apply zenon_H134. apply sym_equal. exact zenon_Hf2. % 3.86/4.03 apply zenon_H9a. apply refl_equal. % 3.86/4.03 apply zenon_H9a. apply refl_equal. % 3.86/4.03 (* end of lemma zenon_L87_ *) % 3.86/4.03 assert (zenon_L88_ : (~((op (op (e3) (e3)) (op (e3) (e3))) = (op (e1) (e1)))) -> ((op (e3) (e3)) = (e1)) -> False). % 3.86/4.03 do 0 intro. intros zenon_H135 zenon_H68. % 3.86/4.03 cut (((op (e3) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H136]. % 3.86/4.03 cut (((op (e3) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H136]. % 3.86/4.03 congruence. % 3.86/4.03 exact (zenon_H136 zenon_H68). % 3.86/4.03 exact (zenon_H136 zenon_H68). % 3.86/4.03 (* end of lemma zenon_L88_ *) % 3.86/4.03 assert (zenon_L89_ : ((op (e1) (e1)) = (e0)) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (op (op (e3) (e3)) (op (e3) (e3))))) -> False). % 3.86/4.03 do 0 intro. intros zenon_H137 zenon_H68 zenon_Ha6. % 3.86/4.03 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H7c | zenon_intro zenon_H7d ]. % 3.86/4.03 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((e0) = (op (op (e3) (e3)) (op (e3) (e3))))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_Ha6. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H7c. % 3.86/4.03 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H7d]. % 3.86/4.03 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Ha7]. % 3.86/4.03 congruence. % 3.86/4.03 cut (((op (e1) (e1)) = (e0)) = ((op (op (e3) (e3)) (op (e3) (e3))) = (e0))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_Ha7. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H137. % 3.86/4.03 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H47]. % 3.86/4.03 cut (((op (e1) (e1)) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H138]. % 3.86/4.03 congruence. % 3.86/4.03 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H7c | zenon_intro zenon_H7d ]. % 3.86/4.03 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((op (e1) (e1)) = (op (op (e3) (e3)) (op (e3) (e3))))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H138. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H7c. % 3.86/4.03 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H7d]. % 3.86/4.03 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H135]. % 3.86/4.03 congruence. % 3.86/4.03 apply (zenon_L88_); trivial. % 3.86/4.03 apply zenon_H7d. apply refl_equal. % 3.86/4.03 apply zenon_H7d. apply refl_equal. % 3.86/4.03 apply zenon_H47. apply refl_equal. % 3.86/4.03 apply zenon_H7d. apply refl_equal. % 3.86/4.03 apply zenon_H7d. apply refl_equal. % 3.86/4.03 (* end of lemma zenon_L89_ *) % 3.86/4.03 assert (zenon_L90_ : ((op (e1) (e1)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> False). % 3.86/4.03 do 0 intro. intros zenon_H137 zenon_H139 zenon_H68. % 3.86/4.03 apply (zenon_notand_s _ _ ax9); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H13a ]. % 3.86/4.03 apply (zenon_L89_); trivial. % 3.86/4.03 apply (zenon_notand_s _ _ zenon_H13a); [ zenon_intro zenon_H13b | zenon_intro zenon_H8b ]. % 3.86/4.03 elim (classic ((op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))))); [ zenon_intro zenon_H84 | zenon_intro zenon_H85 ]. % 3.86/4.03 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) = ((e2) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H13b. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H84. % 3.86/4.03 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 3.86/4.03 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H13c]. % 3.86/4.03 congruence. % 3.86/4.03 cut (((op (e0) (e1)) = (e2)) = ((op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))) = (e2))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H13c. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H139. % 3.86/4.03 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 3.86/4.03 cut (((op (e0) (e1)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H13d]. % 3.86/4.03 congruence. % 3.86/4.03 elim (classic ((op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))))); [ zenon_intro zenon_H84 | zenon_intro zenon_H85 ]. % 3.86/4.03 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3)))) = ((op (e0) (e1)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H13d. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H84. % 3.86/4.03 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))) = (op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 3.86/4.03 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (op (e3) (e3))) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H13e]. % 3.86/4.03 congruence. % 3.86/4.03 cut (((op (e3) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H136]. % 3.86/4.03 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Ha7]. % 3.86/4.03 congruence. % 3.86/4.03 cut (((op (e1) (e1)) = (e0)) = ((op (op (e3) (e3)) (op (e3) (e3))) = (e0))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_Ha7. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H137. % 3.86/4.03 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H47]. % 3.86/4.03 cut (((op (e1) (e1)) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H138]. % 3.86/4.03 congruence. % 3.86/4.03 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H7c | zenon_intro zenon_H7d ]. % 3.86/4.03 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((op (e1) (e1)) = (op (op (e3) (e3)) (op (e3) (e3))))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H138. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H7c. % 3.86/4.03 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H7d]. % 3.86/4.03 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H135]. % 3.86/4.03 congruence. % 3.86/4.03 apply (zenon_L88_); trivial. % 3.86/4.03 apply zenon_H7d. apply refl_equal. % 3.86/4.03 apply zenon_H7d. apply refl_equal. % 3.86/4.03 apply zenon_H47. apply refl_equal. % 3.86/4.03 exact (zenon_H136 zenon_H68). % 3.86/4.03 apply zenon_H85. apply refl_equal. % 3.86/4.03 apply zenon_H85. apply refl_equal. % 3.86/4.03 apply zenon_H4f. apply refl_equal. % 3.86/4.03 apply zenon_H85. apply refl_equal. % 3.86/4.03 apply zenon_H85. apply refl_equal. % 3.86/4.03 apply zenon_H8b. apply sym_equal. exact zenon_H68. % 3.86/4.03 (* end of lemma zenon_L90_ *) % 3.86/4.03 assert (zenon_L91_ : (((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 (e0) (e1)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> False). % 3.86/4.03 do 0 intro. intros zenon_Hde zenon_H10b zenon_H10a zenon_H139 zenon_H137 zenon_H32 zenon_H89 zenon_He1 zenon_Hf6. % 3.86/4.03 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_Hda | zenon_intro zenon_Hdf ]. % 3.86/4.03 apply (zenon_L69_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H68 | zenon_intro zenon_He0 ]. % 3.86/4.03 apply (zenon_L90_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H78 | zenon_intro zenon_H39 ]. % 3.86/4.03 apply (zenon_L73_); trivial. % 3.86/4.03 apply (zenon_L74_); trivial. % 3.86/4.03 (* end of lemma zenon_L91_ *) % 3.86/4.03 assert (zenon_L92_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e1)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e1)) -> ((op (e2) (e2)) = (e3)) -> False). % 3.86/4.03 do 0 intro. intros zenon_H125 zenon_H4a zenon_Hf6 zenon_He1 zenon_H89 zenon_H137 zenon_H139 zenon_H10a zenon_Hde zenon_H32 zenon_H61 zenon_Hd7 zenon_Hd0. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H22 | zenon_intro zenon_H126 ]. % 3.86/4.03 apply (zenon_L49_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H10b | zenon_intro zenon_H127 ]. % 3.86/4.03 apply (zenon_L91_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hda ]. % 3.86/4.03 apply (zenon_L78_); trivial. % 3.86/4.03 apply (zenon_L79_); trivial. % 3.86/4.03 (* end of lemma zenon_L92_ *) % 3.86/4.03 assert (zenon_L93_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e1)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (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) (e3)) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 3.86/4.03 do 0 intro. intros zenon_H125 zenon_H21 zenon_H20 zenon_Hf6 zenon_He1 zenon_H89 zenon_H137 zenon_H139 zenon_Hde zenon_H61 zenon_H12e zenon_H10a zenon_Hf1 zenon_H32 zenon_H128 zenon_H12c. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H22 | zenon_intro zenon_H126 ]. % 3.86/4.03 apply (zenon_L2_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H10b | zenon_intro zenon_H127 ]. % 3.86/4.03 apply (zenon_L91_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hda ]. % 3.86/4.03 apply (zenon_L78_); trivial. % 3.86/4.03 apply (zenon_L83_); trivial. % 3.86/4.03 (* end of lemma zenon_L93_ *) % 3.86/4.03 assert (zenon_L94_ : (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e2)) = (e0)) -> False). % 3.86/4.03 do 0 intro. intros zenon_Hae zenon_H21 zenon_H80. % 3.86/4.03 cut (((op (e0) (e2)) = (e0)) = ((op (e0) (e2)) = (op (e1) (e2)))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_Hae. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H21. % 3.86/4.03 cut (((e0) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H13f]. % 3.86/4.03 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H24]. % 3.86/4.03 congruence. % 3.86/4.03 apply zenon_H24. apply refl_equal. % 3.86/4.03 apply zenon_H13f. apply sym_equal. exact zenon_H80. % 3.86/4.03 (* end of lemma zenon_L94_ *) % 3.86/4.03 assert (zenon_L95_ : (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e2) (e1)) = (e0)) -> False). % 3.86/4.03 do 0 intro. intros zenon_H140 zenon_H48 zenon_Ha1. % 3.86/4.03 cut (((op (e2) (e0)) = (e0)) = ((op (e2) (e0)) = (op (e2) (e1)))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H140. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H48. % 3.86/4.03 cut (((e0) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H141]. % 3.86/4.03 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 3.86/4.03 congruence. % 3.86/4.03 apply zenon_H9a. apply refl_equal. % 3.86/4.03 apply zenon_H141. apply sym_equal. exact zenon_Ha1. % 3.86/4.03 (* end of lemma zenon_L95_ *) % 3.86/4.03 assert (zenon_L96_ : (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e1)) = (e0)) -> False). % 3.86/4.03 do 0 intro. intros zenon_H9b zenon_Hf6 zenon_H142. % 3.86/4.03 cut (((op (e3) (e1)) = (e3)) = ((e0) = (e3))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H9b. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_Hf6. % 3.86/4.03 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H5b]. % 3.86/4.03 cut (((op (e3) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H143]. % 3.86/4.03 congruence. % 3.86/4.03 exact (zenon_H143 zenon_H142). % 3.86/4.03 apply zenon_H5b. apply refl_equal. % 3.86/4.03 (* end of lemma zenon_L96_ *) % 3.86/4.03 assert (zenon_L97_ : ((op (e0) (e2)) = (e0)) -> ((op (e0) (e2)) = (e2)) -> (~((e0) = (e2))) -> False). % 3.86/4.03 do 0 intro. intros zenon_H21 zenon_Haf zenon_H61. % 3.86/4.03 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H62 | zenon_intro zenon_H4f ]. % 3.86/4.03 cut (((e2) = (e2)) = ((e0) = (e2))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H61. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H62. % 3.86/4.03 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 3.86/4.03 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H63]. % 3.86/4.03 congruence. % 3.86/4.03 cut (((op (e0) (e2)) = (e0)) = ((e2) = (e0))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H63. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H21. % 3.86/4.03 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H47]. % 3.86/4.03 cut (((op (e0) (e2)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H144]. % 3.86/4.03 congruence. % 3.86/4.03 exact (zenon_H144 zenon_Haf). % 3.86/4.03 apply zenon_H47. apply refl_equal. % 3.86/4.03 apply zenon_H4f. apply refl_equal. % 3.86/4.03 apply zenon_H4f. apply refl_equal. % 3.86/4.03 (* end of lemma zenon_L97_ *) % 3.86/4.03 assert (zenon_L98_ : ((op (e2) (e3)) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 3.86/4.03 do 0 intro. intros zenon_H32 zenon_H60 zenon_Hc2. % 3.86/4.03 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H108 | zenon_intro zenon_H8c ]. % 3.86/4.03 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e0) (e3)) = (op (e2) (e3)))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_Hc2. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H108. % 3.86/4.03 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H8c]. % 3.86/4.03 cut (((op (e2) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H145]. % 3.86/4.03 congruence. % 3.86/4.03 cut (((op (e2) (e3)) = (e2)) = ((op (e2) (e3)) = (op (e0) (e3)))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H145. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H32. % 3.86/4.03 cut (((e2) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H146]. % 3.86/4.03 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H8c]. % 3.86/4.03 congruence. % 3.86/4.03 apply zenon_H8c. apply refl_equal. % 3.86/4.03 apply zenon_H146. apply sym_equal. exact zenon_H60. % 3.86/4.03 apply zenon_H8c. apply refl_equal. % 3.86/4.03 apply zenon_H8c. apply refl_equal. % 3.86/4.03 (* end of lemma zenon_L98_ *) % 3.86/4.03 assert (zenon_L99_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e3)) = (e1)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 3.86/4.03 do 0 intro. intros zenon_H147 zenon_H36 zenon_H107 zenon_H97 zenon_Hd4 zenon_H11a zenon_Hf6 zenon_H9b zenon_H140 zenon_H48 zenon_Hde zenon_H10a zenon_H89 zenon_He1 zenon_H148 zenon_H149 zenon_Hae zenon_H14a zenon_Hf8 zenon_Hd7 zenon_H4a zenon_H125 zenon_H20 zenon_H12e zenon_Hf1 zenon_H128 zenon_H131 zenon_H14b zenon_H61 zenon_H21 zenon_H32 zenon_Hc2. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14c ]. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H14d ]. % 3.86/4.03 apply (zenon_L62_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H14e ]. % 3.86/4.03 apply (zenon_L63_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H12c ]. % 3.86/4.03 apply (zenon_L80_); trivial. % 3.86/4.03 apply (zenon_L86_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H139 | zenon_intro zenon_H14f ]. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_Hf2 | zenon_intro zenon_H150 ]. % 3.86/4.03 apply (zenon_L87_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H137 | zenon_intro zenon_H151 ]. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H14d ]. % 3.86/4.03 apply (zenon_L62_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H14e ]. % 3.86/4.03 apply (zenon_L63_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H12c ]. % 3.86/4.03 apply (zenon_L92_); trivial. % 3.86/4.03 apply (zenon_L93_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H80 | zenon_intro zenon_H10b ]. % 3.86/4.03 apply (zenon_L94_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H153 | zenon_intro zenon_H152 ]. % 3.86/4.03 exact (zenon_H148 zenon_H153). % 3.86/4.03 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H137 | zenon_intro zenon_H154 ]. % 3.86/4.03 apply (zenon_L91_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H154); [ zenon_intro zenon_Ha1 | zenon_intro zenon_H142 ]. % 3.86/4.03 apply (zenon_L95_); trivial. % 3.86/4.03 apply (zenon_L96_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_Haf | zenon_intro zenon_H60 ]. % 3.86/4.03 apply (zenon_L97_); trivial. % 3.86/4.03 apply (zenon_L98_); trivial. % 3.86/4.03 (* end of lemma zenon_L99_ *) % 3.86/4.03 assert (zenon_L100_ : (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> ((op (e2) (e3)) = (e1)) -> False). % 3.86/4.03 do 0 intro. intros zenon_H50 zenon_H32 zenon_H8a. % 3.86/4.03 cut (((op (e2) (e3)) = (e2)) = ((e1) = (e2))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H50. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H32. % 3.86/4.03 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 3.86/4.03 cut (((op (e2) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H155]. % 3.86/4.03 congruence. % 3.86/4.03 exact (zenon_H155 zenon_H8a). % 3.86/4.03 apply zenon_H4f. apply refl_equal. % 3.86/4.03 (* end of lemma zenon_L100_ *) % 3.86/4.03 assert (zenon_L101_ : (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e3) (e3)) = (e1)) -> False). % 3.86/4.03 do 0 intro. intros zenon_Hd9 zenon_Hd7 zenon_H68. % 3.86/4.03 cut (((op (e0) (e3)) = (e1)) = ((op (e0) (e3)) = (op (e3) (e3)))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_Hd9. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_Hd7. % 3.86/4.03 cut (((e1) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 3.86/4.03 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 3.86/4.03 congruence. % 3.86/4.03 apply zenon_Hc5. apply refl_equal. % 3.86/4.03 apply zenon_H8b. apply sym_equal. exact zenon_H68. % 3.86/4.03 (* end of lemma zenon_L101_ *) % 3.86/4.03 assert (zenon_L102_ : (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e3) (e3)) = (e1)) -> False). % 3.86/4.03 do 0 intro. intros zenon_H10a zenon_H27 zenon_H68. % 3.86/4.03 cut (((op (e1) (e3)) = (e1)) = ((op (e1) (e3)) = (op (e3) (e3)))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H10a. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H27. % 3.86/4.03 cut (((e1) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 3.86/4.03 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 3.86/4.03 congruence. % 3.86/4.03 apply zenon_H2b. apply refl_equal. % 3.86/4.03 apply zenon_H8b. apply sym_equal. exact zenon_H68. % 3.86/4.03 (* end of lemma zenon_L102_ *) % 3.86/4.03 assert (zenon_L103_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e1) (e3)) = (e3)) -> False). % 3.86/4.03 do 0 intro. intros zenon_H156 zenon_Hca zenon_H12b. % 3.86/4.03 cut (((op (e0) (e3)) = (e3)) = ((op (e0) (e3)) = (op (e1) (e3)))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H156. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_Hca. % 3.86/4.03 cut (((e3) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H157]. % 3.86/4.03 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 3.86/4.03 congruence. % 3.86/4.03 apply zenon_Hc5. apply refl_equal. % 3.86/4.03 apply zenon_H157. apply sym_equal. exact zenon_H12b. % 3.86/4.03 (* end of lemma zenon_L103_ *) % 3.86/4.03 assert (zenon_L104_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e3)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 3.86/4.03 do 0 intro. intros zenon_H12e zenon_Hd0 zenon_H68 zenon_H10a zenon_H128 zenon_H32 zenon_H156 zenon_Hca. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H10b | zenon_intro zenon_H12f ]. % 3.86/4.03 apply (zenon_L72_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H27 | zenon_intro zenon_H130 ]. % 3.86/4.03 apply (zenon_L102_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H69 | zenon_intro zenon_H12b ]. % 3.86/4.03 apply (zenon_L81_); trivial. % 3.86/4.03 apply (zenon_L103_); trivial. % 3.86/4.03 (* end of lemma zenon_L104_ *) % 3.86/4.03 assert (zenon_L105_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e3)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 3.86/4.03 do 0 intro. intros zenon_H158 zenon_H21 zenon_H20 zenon_Hd9 zenon_Hc2 zenon_H12e zenon_Hd0 zenon_H68 zenon_H10a zenon_H128 zenon_H32 zenon_H156. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H22 | zenon_intro zenon_H159 ]. % 3.86/4.03 apply (zenon_L2_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H159); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H15a ]. % 3.86/4.03 apply (zenon_L101_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_H60 | zenon_intro zenon_Hca ]. % 3.86/4.03 apply (zenon_L98_); trivial. % 3.86/4.03 apply (zenon_L104_); trivial. % 3.86/4.03 (* end of lemma zenon_L105_ *) % 3.86/4.03 assert (zenon_L106_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (e1))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 3.86/4.03 do 0 intro. intros zenon_He3 zenon_H61 zenon_H14b zenon_H131 zenon_H125 zenon_H4a zenon_Hf8 zenon_H14a zenon_Hae zenon_H149 zenon_H148 zenon_He1 zenon_H89 zenon_Hde zenon_H48 zenon_H140 zenon_H9b zenon_Hf6 zenon_H11a zenon_Hd4 zenon_H97 zenon_H107 zenon_H36 zenon_H147 zenon_Hf1 zenon_H50 zenon_H158 zenon_H21 zenon_H20 zenon_Hd9 zenon_Hc2 zenon_H12e zenon_Hd0 zenon_H10a zenon_H128 zenon_H32 zenon_H156. % 3.86/4.03 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He4 ]. % 3.86/4.03 apply (zenon_L99_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H27 | zenon_intro zenon_He5 ]. % 3.86/4.03 exact (zenon_Hf1 zenon_H27). % 3.86/4.03 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_H8a | zenon_intro zenon_H68 ]. % 3.86/4.03 apply (zenon_L100_); trivial. % 3.86/4.03 apply (zenon_L105_); trivial. % 3.86/4.03 (* end of lemma zenon_L106_ *) % 3.86/4.03 assert (zenon_L107_ : ((op (e0) (e1)) = (e1)) -> ((op (e0) (e1)) = (e2)) -> (~((e1) = (e2))) -> False). % 3.86/4.03 do 0 intro. intros zenon_H57 zenon_H139 zenon_H50. % 3.86/4.03 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H62 | zenon_intro zenon_H4f ]. % 3.86/4.03 cut (((e2) = (e2)) = ((e1) = (e2))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H50. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H62. % 3.86/4.03 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 3.86/4.03 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H15b]. % 3.86/4.03 congruence. % 3.86/4.03 cut (((op (e0) (e1)) = (e1)) = ((e2) = (e1))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H15b. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H57. % 3.86/4.03 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 3.86/4.03 cut (((op (e0) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H15c]. % 3.86/4.03 congruence. % 3.86/4.03 exact (zenon_H15c zenon_H139). % 3.86/4.03 apply zenon_H4c. apply refl_equal. % 3.86/4.03 apply zenon_H4f. apply refl_equal. % 3.86/4.03 apply zenon_H4f. apply refl_equal. % 3.86/4.03 (* end of lemma zenon_L107_ *) % 3.86/4.03 assert (zenon_L108_ : ((op (e0) (e2)) = (e0)) -> ((op (e0) (e2)) = (e1)) -> (~((e0) = (e1))) -> False). % 3.86/4.03 do 0 intro. intros zenon_H21 zenon_Ha4 zenon_H4a. % 3.86/4.03 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H4b | zenon_intro zenon_H4c ]. % 3.86/4.03 cut (((e1) = (e1)) = ((e0) = (e1))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H4a. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H4b. % 3.86/4.03 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 3.86/4.03 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 3.86/4.03 congruence. % 3.86/4.03 cut (((op (e0) (e2)) = (e0)) = ((e1) = (e0))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H4d. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H21. % 3.86/4.03 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H47]. % 3.86/4.03 cut (((op (e0) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H15d]. % 3.86/4.03 congruence. % 3.86/4.03 exact (zenon_H15d zenon_Ha4). % 3.86/4.03 apply zenon_H47. apply refl_equal. % 3.86/4.03 apply zenon_H4c. apply refl_equal. % 3.86/4.03 apply zenon_H4c. apply refl_equal. % 3.86/4.03 (* end of lemma zenon_L108_ *) % 3.86/4.03 assert (zenon_L109_ : (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e3) (e3)) = (e0)) -> False). % 3.86/4.03 do 0 intro. intros zenon_H15e zenon_H15f zenon_Hda. % 3.86/4.03 cut (((op (e3) (e0)) = (e0)) = ((op (e3) (e0)) = (op (e3) (e3)))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H15e. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H15f. % 3.86/4.03 cut (((e0) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 3.86/4.03 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H160]. % 3.86/4.03 congruence. % 3.86/4.03 apply zenon_H160. apply refl_equal. % 3.86/4.03 apply zenon_Hdb. apply sym_equal. exact zenon_Hda. % 3.86/4.03 (* end of lemma zenon_L109_ *) % 3.86/4.03 assert (zenon_L110_ : (((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 (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> False). % 3.86/4.03 do 0 intro. intros zenon_Hde zenon_H15f zenon_H15e zenon_Hd7 zenon_Hd9 zenon_H32 zenon_H89 zenon_He1 zenon_Hf6. % 3.86/4.03 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_Hda | zenon_intro zenon_Hdf ]. % 3.86/4.03 apply (zenon_L109_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H68 | zenon_intro zenon_He0 ]. % 3.86/4.03 apply (zenon_L101_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H78 | zenon_intro zenon_H39 ]. % 3.86/4.03 apply (zenon_L73_); trivial. % 3.86/4.03 apply (zenon_L74_); trivial. % 3.86/4.03 (* end of lemma zenon_L110_ *) % 3.86/4.03 assert (zenon_L111_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (e1))) -> (~((e1) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e1) (e3)) = (e0)) -> False). % 3.86/4.03 do 0 intro. intros zenon_He3 zenon_Hf6 zenon_He1 zenon_H89 zenon_Hd9 zenon_H15e zenon_H15f zenon_Hde zenon_Hf1 zenon_H50 zenon_Hd4 zenon_H21 zenon_Ha3 zenon_Hfe zenon_Hb2 zenon_H107 zenon_H32 zenon_H10b. % 3.86/4.03 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He4 ]. % 3.86/4.03 apply (zenon_L110_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H27 | zenon_intro zenon_He5 ]. % 3.86/4.03 exact (zenon_Hf1 zenon_H27). % 3.86/4.03 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_H8a | zenon_intro zenon_H68 ]. % 3.86/4.03 apply (zenon_L100_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H98 | zenon_intro zenon_Hd5 ]. % 3.86/4.03 apply (zenon_L34_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H7a | zenon_intro zenon_Hd6 ]. % 3.86/4.03 apply (zenon_L67_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H40 | zenon_intro zenon_Hd0 ]. % 3.86/4.03 apply (zenon_L68_); trivial. % 3.86/4.03 apply (zenon_L72_); trivial. % 3.86/4.03 (* end of lemma zenon_L111_ *) % 3.86/4.03 assert (zenon_L112_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e0)) -> ((op (e2) (e2)) = (e3)) -> False). % 3.86/4.03 do 0 intro. intros zenon_He3 zenon_Hf6 zenon_He1 zenon_H89 zenon_Hd9 zenon_H15e zenon_H15f zenon_Hde zenon_Hf1 zenon_H32 zenon_H50 zenon_H10b zenon_Hd0. % 3.86/4.03 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He4 ]. % 3.86/4.03 apply (zenon_L110_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H27 | zenon_intro zenon_He5 ]. % 3.86/4.03 exact (zenon_Hf1 zenon_H27). % 3.86/4.03 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_H8a | zenon_intro zenon_H68 ]. % 3.86/4.03 apply (zenon_L100_); trivial. % 3.86/4.03 apply (zenon_L72_); trivial. % 3.86/4.03 (* end of lemma zenon_L112_ *) % 3.86/4.03 assert (zenon_L113_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (e1))) -> (((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 (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (e3))) -> False). % 3.86/4.03 do 0 intro. intros zenon_H11a zenon_H9b zenon_H107 zenon_Hfe zenon_Ha3 zenon_H21 zenon_Hd4 zenon_H10b zenon_H50 zenon_H32 zenon_Hf1 zenon_Hde zenon_H15f zenon_H15e zenon_Hd9 zenon_H89 zenon_He1 zenon_Hf6 zenon_He3 zenon_H36. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H11a); [ zenon_intro zenon_Hbb | zenon_intro zenon_H11b ]. % 3.86/4.03 apply (zenon_L64_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_Hb2 | zenon_intro zenon_H11c ]. % 3.86/4.03 apply (zenon_L111_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H5d ]. % 3.86/4.03 apply (zenon_L112_); trivial. % 3.86/4.03 exact (zenon_H36 zenon_H5d). % 3.86/4.03 (* end of lemma zenon_L113_ *) % 3.86/4.03 assert (zenon_L114_ : ((op (e1) (e2)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> False). % 3.86/4.03 do 0 intro. intros zenon_H3d zenon_H28 zenon_H161. % 3.86/4.03 elim (classic ((op (e1) (e2)) = (op (e1) (e2)))); [ zenon_intro zenon_H162 | zenon_intro zenon_Had ]. % 3.86/4.03 cut (((op (e1) (e2)) = (op (e1) (e2))) = ((op (e1) (e0)) = (op (e1) (e2)))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H161. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H162. % 3.86/4.03 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Had]. % 3.86/4.03 cut (((op (e1) (e2)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H163]. % 3.86/4.03 congruence. % 3.86/4.03 cut (((op (e1) (e2)) = (e1)) = ((op (e1) (e2)) = (op (e1) (e0)))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H163. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H3d. % 3.86/4.03 cut (((e1) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2d]. % 3.86/4.03 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Had]. % 3.86/4.03 congruence. % 3.86/4.03 apply zenon_Had. apply refl_equal. % 3.86/4.03 apply zenon_H2d. apply sym_equal. exact zenon_H28. % 3.86/4.03 apply zenon_Had. apply refl_equal. % 3.86/4.03 apply zenon_Had. apply refl_equal. % 3.86/4.03 (* end of lemma zenon_L114_ *) % 3.86/4.03 assert (zenon_L115_ : (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> False). % 3.86/4.03 do 0 intro. intros zenon_H164 zenon_Hf6 zenon_H5d. % 3.86/4.03 cut (((op (e3) (e1)) = (e3)) = ((op (e3) (e1)) = (op (e3) (e2)))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H164. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_Hf6. % 3.86/4.03 cut (((e3) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H165]. % 3.86/4.03 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_He2]. % 3.86/4.03 congruence. % 3.86/4.03 apply zenon_He2. apply refl_equal. % 3.86/4.03 apply zenon_H165. apply sym_equal. exact zenon_H5d. % 3.86/4.03 (* end of lemma zenon_L115_ *) % 3.86/4.03 assert (zenon_L116_ : (((op (e3) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 3.86/4.03 do 0 intro. intros zenon_H166 zenon_Hf6 zenon_H164. % 3.86/4.03 apply (zenon_and_s _ _ zenon_H166). zenon_intro zenon_H5d. zenon_intro zenon_H91. % 3.86/4.03 apply (zenon_L115_); trivial. % 3.86/4.03 (* end of lemma zenon_L116_ *) % 3.86/4.03 assert (zenon_L117_ : ((op (e0) (e2)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> False). % 3.86/4.03 do 0 intro. intros zenon_H21 zenon_H153 zenon_H167. % 3.86/4.03 elim (classic ((op (e0) (e2)) = (op (e0) (e2)))); [ zenon_intro zenon_H168 | zenon_intro zenon_H24 ]. % 3.86/4.03 cut (((op (e0) (e2)) = (op (e0) (e2))) = ((op (e0) (e1)) = (op (e0) (e2)))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H167. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H168. % 3.86/4.03 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H24]. % 3.86/4.03 cut (((op (e0) (e2)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H169]. % 3.86/4.03 congruence. % 3.86/4.03 cut (((op (e0) (e2)) = (e0)) = ((op (e0) (e2)) = (op (e0) (e1)))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H169. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H21. % 3.86/4.03 cut (((e0) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 3.86/4.03 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H24]. % 3.86/4.03 congruence. % 3.86/4.03 apply zenon_H24. apply refl_equal. % 3.86/4.03 apply zenon_H16a. apply sym_equal. exact zenon_H153. % 3.86/4.03 apply zenon_H24. apply refl_equal. % 3.86/4.03 apply zenon_H24. apply refl_equal. % 3.86/4.03 (* end of lemma zenon_L117_ *) % 3.86/4.03 assert (zenon_L118_ : (((op (e0) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> False). % 3.86/4.03 do 0 intro. intros zenon_H16b zenon_H153 zenon_H167. % 3.86/4.03 apply (zenon_and_s _ _ zenon_H16b). zenon_intro zenon_H21. zenon_intro zenon_H16c. % 3.86/4.03 apply (zenon_L117_); trivial. % 3.86/4.03 (* end of lemma zenon_L118_ *) % 3.86/4.03 assert (zenon_L119_ : (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e0) (e3)) = (e0)) -> False). % 3.86/4.03 do 0 intro. intros zenon_H16d zenon_H153 zenon_H22. % 3.86/4.03 cut (((op (e0) (e1)) = (e0)) = ((op (e0) (e1)) = (op (e0) (e3)))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H16d. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H153. % 3.86/4.03 cut (((e0) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H23]. % 3.86/4.03 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 3.86/4.03 congruence. % 3.86/4.03 apply zenon_H5a. apply refl_equal. % 3.86/4.03 apply zenon_H23. apply sym_equal. exact zenon_H22. % 3.86/4.03 (* end of lemma zenon_L119_ *) % 3.86/4.03 assert (zenon_L120_ : (((op (e0) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> False). % 3.86/4.03 do 0 intro. intros zenon_H25 zenon_H153 zenon_H16d. % 3.86/4.03 apply (zenon_and_s _ _ zenon_H25). zenon_intro zenon_H22. zenon_intro zenon_H26. % 3.86/4.03 apply (zenon_L119_); trivial. % 3.86/4.03 (* end of lemma zenon_L120_ *) % 3.86/4.03 assert (zenon_L121_ : (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> False). % 3.86/4.03 do 0 intro. intros zenon_H16e zenon_H3d zenon_H27. % 3.86/4.03 cut (((op (e1) (e2)) = (e1)) = ((op (e1) (e2)) = (op (e1) (e3)))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H16e. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H3d. % 3.86/4.03 cut (((e1) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H16f]. % 3.86/4.03 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Had]. % 3.86/4.03 congruence. % 3.86/4.03 apply zenon_Had. apply refl_equal. % 3.86/4.03 apply zenon_H16f. apply sym_equal. exact zenon_H27. % 3.86/4.03 (* end of lemma zenon_L121_ *) % 3.86/4.03 assert (zenon_L122_ : (((op (e1) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> False). % 3.86/4.03 do 0 intro. intros zenon_H2e zenon_H3d zenon_H16e. % 3.86/4.03 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H27. zenon_intro zenon_H2f. % 3.86/4.03 apply (zenon_L121_); trivial. % 3.86/4.03 (* end of lemma zenon_L122_ *) % 3.86/4.03 assert (zenon_L123_ : ((op (e2) (e3)) = (e2)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> False). % 3.86/4.03 do 0 intro. intros zenon_H32 zenon_H170 zenon_H171. % 3.86/4.03 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H108 | zenon_intro zenon_H8c ]. % 3.86/4.03 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e2) (e0)) = (op (e2) (e3)))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H171. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H108. % 3.86/4.03 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H8c]. % 3.86/4.03 cut (((op (e2) (e3)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H172]. % 3.86/4.03 congruence. % 3.86/4.03 cut (((op (e2) (e3)) = (e2)) = ((op (e2) (e3)) = (op (e2) (e0)))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H172. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H32. % 3.86/4.03 cut (((e2) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H173]. % 3.86/4.03 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H8c]. % 3.86/4.03 congruence. % 3.86/4.03 apply zenon_H8c. apply refl_equal. % 3.86/4.03 apply zenon_H173. apply sym_equal. exact zenon_H170. % 3.86/4.03 apply zenon_H8c. apply refl_equal. % 3.86/4.03 apply zenon_H8c. apply refl_equal. % 3.86/4.03 (* end of lemma zenon_L123_ *) % 3.86/4.03 assert (zenon_L124_ : (((op (e2) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> False). % 3.86/4.03 do 0 intro. intros zenon_H35 zenon_H170 zenon_H171. % 3.86/4.03 apply (zenon_and_s _ _ zenon_H35). zenon_intro zenon_H32. zenon_intro zenon_H36. % 3.86/4.03 apply (zenon_L123_); trivial. % 3.86/4.03 (* end of lemma zenon_L124_ *) % 3.86/4.03 assert (zenon_L125_ : ((op (e0) (e1)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> False). % 3.86/4.03 do 0 intro. intros zenon_H153 zenon_H174 zenon_H175. % 3.86/4.03 elim (classic ((op (e0) (e1)) = (op (e0) (e1)))); [ zenon_intro zenon_H176 | zenon_intro zenon_H5a ]. % 3.86/4.03 cut (((op (e0) (e1)) = (op (e0) (e1))) = ((op (e0) (e0)) = (op (e0) (e1)))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H175. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H176. % 3.86/4.03 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 3.86/4.03 cut (((op (e0) (e1)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H177]. % 3.86/4.03 congruence. % 3.86/4.03 cut (((op (e0) (e1)) = (e0)) = ((op (e0) (e1)) = (op (e0) (e0)))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H177. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H153. % 3.86/4.03 cut (((e0) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H178]. % 3.86/4.03 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 3.86/4.03 congruence. % 3.86/4.03 apply zenon_H5a. apply refl_equal. % 3.86/4.03 apply zenon_H178. apply sym_equal. exact zenon_H174. % 3.86/4.03 apply zenon_H5a. apply refl_equal. % 3.86/4.03 apply zenon_H5a. apply refl_equal. % 3.86/4.03 (* end of lemma zenon_L125_ *) % 3.86/4.03 assert (zenon_L126_ : ((op (e0) (e0)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> (~((e1) = (e3))) -> False). % 3.86/4.03 do 0 intro. intros zenon_H41 zenon_H66 zenon_H5c. % 3.86/4.03 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H5b ]. % 3.86/4.03 cut (((e3) = (e3)) = ((e1) = (e3))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H5c. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_Hc7. % 3.86/4.03 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H5b]. % 3.86/4.03 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hc8]. % 3.86/4.03 congruence. % 3.86/4.03 cut (((op (e0) (e0)) = (e1)) = ((e3) = (e1))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_Hc8. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H41. % 3.86/4.03 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 3.86/4.03 cut (((op (e0) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 3.86/4.03 congruence. % 3.86/4.03 exact (zenon_H67 zenon_H66). % 3.86/4.03 apply zenon_H4c. apply refl_equal. % 3.86/4.03 apply zenon_H5b. apply refl_equal. % 3.86/4.03 apply zenon_H5b. apply refl_equal. % 3.86/4.03 (* end of lemma zenon_L126_ *) % 3.86/4.03 assert (zenon_L127_ : ((op (e0) (e1)) = (e0)) -> ((op (e0) (e1)) = (e3)) -> (~((e0) = (e3))) -> False). % 3.86/4.03 do 0 intro. intros zenon_H153 zenon_Hc6 zenon_H9b. % 3.86/4.03 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H5b ]. % 3.86/4.03 cut (((e3) = (e3)) = ((e0) = (e3))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H9b. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_Hc7. % 3.86/4.03 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H5b]. % 3.86/4.03 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 3.86/4.03 congruence. % 3.86/4.03 cut (((op (e0) (e1)) = (e0)) = ((e3) = (e0))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_Hcb. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H153. % 3.86/4.03 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H47]. % 3.86/4.03 cut (((op (e0) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hc9]. % 3.86/4.03 congruence. % 3.86/4.03 exact (zenon_Hc9 zenon_Hc6). % 3.86/4.03 apply zenon_H47. apply refl_equal. % 3.86/4.03 apply zenon_H5b. apply refl_equal. % 3.86/4.03 apply zenon_H5b. apply refl_equal. % 3.86/4.03 (* end of lemma zenon_L127_ *) % 3.86/4.03 assert (zenon_L128_ : ((op (e1) (e0)) = (e0)) -> ((op (e1) (e0)) = (e3)) -> (~((e0) = (e3))) -> False). % 3.86/4.03 do 0 intro. intros zenon_Hf2 zenon_H179 zenon_H9b. % 3.86/4.03 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H5b ]. % 3.86/4.03 cut (((e3) = (e3)) = ((e0) = (e3))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H9b. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_Hc7. % 3.86/4.03 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H5b]. % 3.86/4.03 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 3.86/4.03 congruence. % 3.86/4.03 cut (((op (e1) (e0)) = (e0)) = ((e3) = (e0))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_Hcb. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_Hf2. % 3.86/4.03 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H47]. % 3.86/4.03 cut (((op (e1) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H17a]. % 3.86/4.03 congruence. % 3.86/4.03 exact (zenon_H17a zenon_H179). % 3.86/4.03 apply zenon_H47. apply refl_equal. % 3.86/4.03 apply zenon_H5b. apply refl_equal. % 3.86/4.03 apply zenon_H5b. apply refl_equal. % 3.86/4.03 (* end of lemma zenon_L128_ *) % 3.86/4.03 assert (zenon_L129_ : ((op (e0) (e2)) = (e1)) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> False). % 3.86/4.03 do 0 intro. intros zenon_Ha4 zenon_H41 zenon_H17b. % 3.86/4.03 elim (classic ((op (e0) (e2)) = (op (e0) (e2)))); [ zenon_intro zenon_H168 | zenon_intro zenon_H24 ]. % 3.86/4.03 cut (((op (e0) (e2)) = (op (e0) (e2))) = ((op (e0) (e0)) = (op (e0) (e2)))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H17b. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H168. % 3.86/4.03 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H24]. % 3.86/4.03 cut (((op (e0) (e2)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H17c]. % 3.86/4.03 congruence. % 3.86/4.03 cut (((op (e0) (e2)) = (e1)) = ((op (e0) (e2)) = (op (e0) (e0)))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H17c. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_Ha4. % 3.86/4.03 cut (((e1) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 3.86/4.03 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H24]. % 3.86/4.03 congruence. % 3.86/4.03 apply zenon_H24. apply refl_equal. % 3.86/4.03 apply zenon_H46. apply sym_equal. exact zenon_H41. % 3.86/4.03 apply zenon_H24. apply refl_equal. % 3.86/4.03 apply zenon_H24. apply refl_equal. % 3.86/4.03 (* end of lemma zenon_L129_ *) % 3.86/4.03 assert (zenon_L130_ : (~((e0) = (e1))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e2)) = (e0)) -> False). % 3.86/4.03 do 0 intro. intros zenon_H4a zenon_H3d zenon_H80. % 3.86/4.03 cut (((op (e1) (e2)) = (e1)) = ((e0) = (e1))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H4a. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H3d. % 3.86/4.03 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 3.86/4.03 cut (((op (e1) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H17d]. % 3.86/4.03 congruence. % 3.86/4.03 exact (zenon_H17d zenon_H80). % 3.86/4.03 apply zenon_H4c. apply refl_equal. % 3.86/4.03 (* end of lemma zenon_L130_ *) % 3.86/4.03 assert (zenon_L131_ : ((op (e0) (e3)) = (e2)) -> ((op (e0) (e3)) = (e3)) -> (~((e2) = (e3))) -> False). % 3.86/4.03 do 0 intro. intros zenon_H60 zenon_Hca zenon_H17e. % 3.86/4.03 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H5b ]. % 3.86/4.03 cut (((e3) = (e3)) = ((e2) = (e3))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H17e. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_Hc7. % 3.86/4.03 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H5b]. % 3.86/4.03 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H17f]. % 3.86/4.03 congruence. % 3.86/4.03 cut (((op (e0) (e3)) = (e2)) = ((e3) = (e2))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H17f. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H60. % 3.86/4.03 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 3.86/4.03 cut (((op (e0) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hcc]. % 3.86/4.03 congruence. % 3.86/4.03 exact (zenon_Hcc zenon_Hca). % 3.86/4.03 apply zenon_H4f. apply refl_equal. % 3.86/4.03 apply zenon_H5b. apply refl_equal. % 3.86/4.03 apply zenon_H5b. apply refl_equal. % 3.86/4.03 (* end of lemma zenon_L131_ *) % 3.86/4.03 assert (zenon_L132_ : ((op (e1) (e3)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> (~((e1) = (e2))) -> False). % 3.86/4.03 do 0 intro. intros zenon_H27 zenon_H69 zenon_H50. % 3.86/4.03 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H62 | zenon_intro zenon_H4f ]. % 3.86/4.03 cut (((e2) = (e2)) = ((e1) = (e2))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H50. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H62. % 3.86/4.03 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 3.86/4.03 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H15b]. % 3.86/4.03 congruence. % 3.86/4.03 cut (((op (e1) (e3)) = (e1)) = ((e2) = (e1))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H15b. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H27. % 3.86/4.03 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 3.86/4.03 cut (((op (e1) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H180]. % 3.86/4.03 congruence. % 3.86/4.03 exact (zenon_H180 zenon_H69). % 3.86/4.03 apply zenon_H4c. apply refl_equal. % 3.86/4.03 apply zenon_H4f. apply refl_equal. % 3.86/4.03 apply zenon_H4f. apply refl_equal. % 3.86/4.03 (* end of lemma zenon_L132_ *) % 3.86/4.03 assert (zenon_L133_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e3)) = (e2))) -> ((op (e2) (e2)) = (e1)) -> ((op (e1) (e2)) = (e0)) -> False). % 3.86/4.03 do 0 intro. intros zenon_H92 zenon_H17e zenon_Hca zenon_H50 zenon_H27 zenon_H91 zenon_H7a zenon_H80. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H60 | zenon_intro zenon_H95 ]. % 3.86/4.03 apply (zenon_L131_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H69 | zenon_intro zenon_H96 ]. % 3.86/4.03 apply (zenon_L132_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H32 | zenon_intro zenon_H78 ]. % 3.86/4.03 exact (zenon_H91 zenon_H32). % 3.86/4.03 apply (zenon_L26_); trivial. % 3.86/4.03 (* end of lemma zenon_L133_ *) % 3.86/4.03 assert (zenon_L134_ : (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> ((op (e1) (e3)) = (e0)) -> False). % 3.86/4.03 do 0 intro. intros zenon_H4a zenon_H27 zenon_H10b. % 3.86/4.03 cut (((op (e1) (e3)) = (e1)) = ((e0) = (e1))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H4a. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H27. % 3.86/4.03 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 3.86/4.03 cut (((op (e1) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H181]. % 3.86/4.03 congruence. % 3.86/4.03 exact (zenon_H181 zenon_H10b). % 3.86/4.03 apply zenon_H4c. apply refl_equal. % 3.86/4.03 (* end of lemma zenon_L134_ *) % 3.86/4.03 assert (zenon_L135_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e3)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> False). % 3.86/4.03 do 0 intro. intros zenon_H14b zenon_H9b zenon_H179 zenon_H153 zenon_H182 zenon_H5d zenon_H5c zenon_H92 zenon_H17e zenon_Hca zenon_H50 zenon_H91 zenon_H41 zenon_H17b zenon_H183 zenon_H4a zenon_H27. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_Hf2 | zenon_intro zenon_H150 ]. % 3.86/4.03 apply (zenon_L128_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H137 | zenon_intro zenon_H151 ]. % 3.86/4.03 cut (((op (e0) (e1)) = (e0)) = ((op (e0) (e1)) = (op (e1) (e1)))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H182. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H153. % 3.86/4.03 cut (((e0) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H184]. % 3.86/4.03 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 3.86/4.03 congruence. % 3.86/4.03 apply zenon_H5a. apply refl_equal. % 3.86/4.03 apply zenon_H184. apply sym_equal. exact zenon_H137. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H80 | zenon_intro zenon_H10b ]. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H183); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H185 ]. % 3.86/4.03 apply (zenon_L129_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H3d | zenon_intro zenon_H186 ]. % 3.86/4.03 apply (zenon_L130_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H7a | zenon_intro zenon_H5e ]. % 3.86/4.03 apply (zenon_L133_); trivial. % 3.86/4.03 apply (zenon_L19_); trivial. % 3.86/4.03 apply (zenon_L134_); trivial. % 3.86/4.03 (* end of lemma zenon_L135_ *) % 3.86/4.03 assert (zenon_L136_ : ((op (e2) (e0)) = (e2)) -> ((op (e2) (e0)) = (e3)) -> (~((e2) = (e3))) -> False). % 3.86/4.03 do 0 intro. intros zenon_H170 zenon_Hf4 zenon_H17e. % 3.86/4.03 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H5b ]. % 3.86/4.03 cut (((e3) = (e3)) = ((e2) = (e3))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H17e. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_Hc7. % 3.86/4.03 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H5b]. % 3.86/4.03 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H17f]. % 3.86/4.03 congruence. % 3.86/4.03 cut (((op (e2) (e0)) = (e2)) = ((e3) = (e2))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H17f. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H170. % 3.86/4.03 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 3.86/4.03 cut (((op (e2) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 3.86/4.03 congruence. % 3.86/4.03 exact (zenon_Hf5 zenon_Hf4). % 3.86/4.03 apply zenon_H4f. apply refl_equal. % 3.86/4.03 apply zenon_H5b. apply refl_equal. % 3.86/4.03 apply zenon_H5b. apply refl_equal. % 3.86/4.03 (* end of lemma zenon_L136_ *) % 3.86/4.03 assert (zenon_L137_ : (~((e0) = (e3))) -> ((op (e3) (e0)) = (e3)) -> ((op (e3) (e0)) = (e0)) -> False). % 3.86/4.03 do 0 intro. intros zenon_H9b zenon_H187 zenon_H15f. % 3.86/4.03 cut (((op (e3) (e0)) = (e3)) = ((e0) = (e3))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H9b. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H187. % 3.86/4.03 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H5b]. % 3.86/4.03 cut (((op (e3) (e0)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H188]. % 3.86/4.03 congruence. % 3.86/4.03 exact (zenon_H188 zenon_H15f). % 3.86/4.03 apply zenon_H5b. apply refl_equal. % 3.86/4.03 (* end of lemma zenon_L137_ *) % 3.86/4.03 assert (zenon_L138_ : ((op (e0) (e1)) = (e1)) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> False). % 3.86/4.03 do 0 intro. intros zenon_H57 zenon_H41 zenon_H175. % 3.86/4.03 elim (classic ((op (e0) (e1)) = (op (e0) (e1)))); [ zenon_intro zenon_H176 | zenon_intro zenon_H5a ]. % 3.86/4.03 cut (((op (e0) (e1)) = (op (e0) (e1))) = ((op (e0) (e0)) = (op (e0) (e1)))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H175. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H176. % 3.86/4.03 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 3.86/4.03 cut (((op (e0) (e1)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H177]. % 3.86/4.03 congruence. % 3.86/4.03 cut (((op (e0) (e1)) = (e1)) = ((op (e0) (e1)) = (op (e0) (e0)))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H177. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H57. % 3.86/4.03 cut (((e1) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 3.86/4.03 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 3.86/4.03 congruence. % 3.86/4.03 apply zenon_H5a. apply refl_equal. % 3.86/4.03 apply zenon_H46. apply sym_equal. exact zenon_H41. % 3.86/4.03 apply zenon_H5a. apply refl_equal. % 3.86/4.03 apply zenon_H5a. apply refl_equal. % 3.86/4.03 (* end of lemma zenon_L138_ *) % 3.86/4.03 assert (zenon_L139_ : (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (e0)) = (e1)) -> False). % 3.86/4.03 do 0 intro. intros zenon_H50 zenon_H170 zenon_H49. % 3.86/4.03 cut (((op (e2) (e0)) = (e2)) = ((e1) = (e2))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H50. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H170. % 3.86/4.03 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 3.86/4.03 cut (((op (e2) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 3.86/4.03 congruence. % 3.86/4.03 exact (zenon_H4e zenon_H49). % 3.86/4.03 apply zenon_H4f. apply refl_equal. % 3.86/4.03 (* end of lemma zenon_L139_ *) % 3.86/4.03 assert (zenon_L140_ : ((op (e3) (e0)) = (e0)) -> ((op (e3) (e0)) = (e1)) -> (~((e0) = (e1))) -> False). % 3.86/4.03 do 0 intro. intros zenon_H15f zenon_H54 zenon_H4a. % 3.86/4.03 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H4b | zenon_intro zenon_H4c ]. % 3.86/4.03 cut (((e1) = (e1)) = ((e0) = (e1))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H4a. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H4b. % 3.86/4.03 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 3.86/4.03 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 3.86/4.03 congruence. % 3.86/4.03 cut (((op (e3) (e0)) = (e0)) = ((e1) = (e0))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H4d. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H15f. % 3.86/4.03 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H47]. % 3.86/4.03 cut (((op (e3) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H189]. % 3.86/4.03 congruence. % 3.86/4.03 exact (zenon_H189 zenon_H54). % 3.86/4.03 apply zenon_H47. apply refl_equal. % 3.86/4.03 apply zenon_H4c. apply refl_equal. % 3.86/4.03 apply zenon_H4c. apply refl_equal. % 3.86/4.03 (* end of lemma zenon_L140_ *) % 3.86/4.03 assert (zenon_L141_ : ((op (e1) (e3)) = (e1)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 3.86/4.03 do 0 intro. intros zenon_H27 zenon_Hd7 zenon_H156. % 3.86/4.03 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H2a | zenon_intro zenon_H2b ]. % 3.86/4.03 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e0) (e3)) = (op (e1) (e3)))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H156. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H2a. % 3.86/4.03 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 3.86/4.03 cut (((op (e1) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H18a]. % 3.86/4.03 congruence. % 3.86/4.03 cut (((op (e1) (e3)) = (e1)) = ((op (e1) (e3)) = (op (e0) (e3)))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H18a. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H27. % 3.86/4.03 cut (((e1) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H18b]. % 3.86/4.03 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 3.86/4.03 congruence. % 3.86/4.03 apply zenon_H2b. apply refl_equal. % 3.86/4.03 apply zenon_H18b. apply sym_equal. exact zenon_Hd7. % 3.86/4.03 apply zenon_H2b. apply refl_equal. % 3.86/4.03 apply zenon_H2b. apply refl_equal. % 3.86/4.03 (* end of lemma zenon_L141_ *) % 3.86/4.03 assert (zenon_L142_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (e2))) -> (((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) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 3.86/4.03 do 0 intro. intros zenon_He8 zenon_H9b zenon_H17e zenon_H14b zenon_H153 zenon_H182 zenon_H5d zenon_H5c zenon_H92 zenon_H91 zenon_H183 zenon_H18c zenon_Hbc zenon_He9 zenon_H175 zenon_H4a zenon_H15f zenon_H50 zenon_H170 zenon_H18d zenon_H17b zenon_H18e zenon_H27 zenon_H156. % 3.86/4.03 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hea ]. % 3.86/4.03 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H66 | zenon_intro zenon_Hec ]. % 3.86/4.03 apply (zenon_L126_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hed ]. % 3.86/4.03 apply (zenon_L127_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hca ]. % 3.86/4.03 apply (zenon_L40_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H66 | zenon_intro zenon_H18f ]. % 3.86/4.03 apply (zenon_L126_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H179 | zenon_intro zenon_H190 ]. % 3.86/4.03 apply (zenon_L135_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H187 ]. % 3.86/4.03 apply (zenon_L136_); trivial. % 3.86/4.03 apply (zenon_L137_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H57 | zenon_intro zenon_Heb ]. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H41 | zenon_intro zenon_H191 ]. % 3.86/4.03 apply (zenon_L138_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_H28 | zenon_intro zenon_H192 ]. % 3.86/4.03 exact (zenon_H18d zenon_H28). % 3.86/4.03 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H49 | zenon_intro zenon_H54 ]. % 3.86/4.03 apply (zenon_L139_); trivial. % 3.86/4.03 apply (zenon_L140_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Ha4 | zenon_intro zenon_Hd7 ]. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H41 | zenon_intro zenon_H191 ]. % 3.86/4.03 apply (zenon_L129_); trivial. % 3.86/4.03 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_H28 | zenon_intro zenon_H192 ]. % 3.86/4.03 exact (zenon_H18d zenon_H28). % 3.86/4.03 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H49 | zenon_intro zenon_H54 ]. % 3.86/4.03 apply (zenon_L139_); trivial. % 3.86/4.03 apply (zenon_L140_); trivial. % 3.86/4.03 apply (zenon_L141_); trivial. % 3.86/4.03 (* end of lemma zenon_L142_ *) % 3.86/4.03 assert (zenon_L143_ : (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> False). % 3.86/4.03 do 0 intro. intros zenon_H56 zenon_H153 zenon_H142. % 3.86/4.03 cut (((op (e0) (e1)) = (e0)) = ((op (e0) (e1)) = (op (e3) (e1)))). % 3.86/4.03 intro zenon_D_pnotp. % 3.86/4.03 apply zenon_H56. % 3.86/4.03 rewrite <- zenon_D_pnotp. % 3.86/4.03 exact zenon_H153. % 3.86/4.04 cut (((e0) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H193]. % 3.86/4.04 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 3.86/4.04 congruence. % 3.86/4.04 apply zenon_H5a. apply refl_equal. % 3.86/4.04 apply zenon_H193. apply sym_equal. exact zenon_H142. % 3.86/4.04 (* end of lemma zenon_L143_ *) % 3.86/4.04 assert (zenon_L144_ : (~((op (op (e1) (e1)) (op (e1) (e1))) = (op (e3) (e3)))) -> ((op (e1) (e1)) = (e3)) -> False). % 3.86/4.04 do 0 intro. intros zenon_H194 zenon_H195. % 3.86/4.04 cut (((op (e1) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H196]. % 3.86/4.04 cut (((op (e1) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H196]. % 3.86/4.04 congruence. % 3.86/4.04 exact (zenon_H196 zenon_H195). % 3.86/4.04 exact (zenon_H196 zenon_H195). % 3.86/4.04 (* end of lemma zenon_L144_ *) % 3.86/4.04 assert (zenon_L145_ : ((op (e3) (e3)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> (~((e0) = (op (op (e1) (e1)) (op (e1) (e1))))) -> False). % 3.86/4.04 do 0 intro. intros zenon_Hda zenon_H195 zenon_H197. % 3.86/4.04 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H198 | zenon_intro zenon_H199 ]. % 3.86/4.04 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((e0) = (op (op (e1) (e1)) (op (e1) (e1))))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H197. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H198. % 3.86/4.04 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H199]. % 3.86/4.04 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H19a]. % 3.86/4.04 congruence. % 3.86/4.04 cut (((op (e3) (e3)) = (e0)) = ((op (op (e1) (e1)) (op (e1) (e1))) = (e0))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H19a. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_Hda. % 3.86/4.04 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H47]. % 3.86/4.04 cut (((op (e3) (e3)) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H19b]. % 3.86/4.04 congruence. % 3.86/4.04 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H198 | zenon_intro zenon_H199 ]. % 3.86/4.04 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((op (e3) (e3)) = (op (op (e1) (e1)) (op (e1) (e1))))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H19b. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H198. % 3.86/4.04 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H199]. % 3.86/4.04 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H194]. % 3.86/4.04 congruence. % 3.86/4.04 apply (zenon_L144_); trivial. % 3.86/4.04 apply zenon_H199. apply refl_equal. % 3.86/4.04 apply zenon_H199. apply refl_equal. % 3.86/4.04 apply zenon_H47. apply refl_equal. % 3.86/4.04 apply zenon_H199. apply refl_equal. % 3.86/4.04 apply zenon_H199. apply refl_equal. % 3.86/4.04 (* end of lemma zenon_L145_ *) % 3.86/4.04 assert (zenon_L146_ : ((op (e3) (e3)) = (e0)) -> ((op (e0) (e3)) = (e2)) -> ((op (e1) (e1)) = (e3)) -> False). % 3.86/4.04 do 0 intro. intros zenon_Hda zenon_H60 zenon_H195. % 3.86/4.04 apply (zenon_notand_s _ _ ax8); [ zenon_intro zenon_H197 | zenon_intro zenon_H19c ]. % 3.86/4.04 apply (zenon_L145_); trivial. % 3.86/4.04 apply (zenon_notand_s _ _ zenon_H19c); [ zenon_intro zenon_H19e | zenon_intro zenon_H19d ]. % 3.86/4.04 elim (classic ((op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))))); [ zenon_intro zenon_H19f | zenon_intro zenon_H1a0 ]. % 3.86/4.04 cut (((op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) = ((e2) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H19e. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H19f. % 3.86/4.04 cut (((op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1a0]. % 3.86/4.04 cut (((op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 3.86/4.04 congruence. % 3.86/4.04 cut (((op (e0) (e3)) = (e2)) = ((op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))) = (e2))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H1a1. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H60. % 3.86/4.04 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 3.86/4.04 cut (((op (e0) (e3)) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1a2]. % 3.86/4.04 congruence. % 3.86/4.04 elim (classic ((op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))))); [ zenon_intro zenon_H19f | zenon_intro zenon_H1a0 ]. % 3.86/4.04 cut (((op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) = ((op (e0) (e3)) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H1a2. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H19f. % 3.86/4.04 cut (((op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1a0]. % 3.86/4.04 cut (((op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1a3]. % 3.86/4.04 congruence. % 3.86/4.04 cut (((op (e1) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H196]. % 3.86/4.04 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H19a]. % 3.86/4.04 congruence. % 3.86/4.04 cut (((op (e3) (e3)) = (e0)) = ((op (op (e1) (e1)) (op (e1) (e1))) = (e0))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H19a. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_Hda. % 3.86/4.04 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H47]. % 3.86/4.04 cut (((op (e3) (e3)) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H19b]. % 3.86/4.04 congruence. % 3.86/4.04 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H198 | zenon_intro zenon_H199 ]. % 3.86/4.04 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((op (e3) (e3)) = (op (op (e1) (e1)) (op (e1) (e1))))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H19b. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H198. % 3.86/4.04 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H199]. % 3.86/4.04 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H194]. % 3.86/4.04 congruence. % 3.86/4.04 apply (zenon_L144_); trivial. % 3.86/4.04 apply zenon_H199. apply refl_equal. % 3.86/4.04 apply zenon_H199. apply refl_equal. % 3.86/4.04 apply zenon_H47. apply refl_equal. % 3.86/4.04 exact (zenon_H196 zenon_H195). % 3.86/4.04 apply zenon_H1a0. apply refl_equal. % 3.86/4.04 apply zenon_H1a0. apply refl_equal. % 3.86/4.04 apply zenon_H4f. apply refl_equal. % 3.86/4.04 apply zenon_H1a0. apply refl_equal. % 3.86/4.04 apply zenon_H1a0. apply refl_equal. % 3.86/4.04 apply zenon_H19d. apply sym_equal. exact zenon_H195. % 3.86/4.04 (* end of lemma zenon_L146_ *) % 3.86/4.04 assert (zenon_L147_ : ((op (e3) (e3)) = (e2)) -> ((op (e1) (e1)) = (e3)) -> (~((e2) = (op (op (e1) (e1)) (op (e1) (e1))))) -> False). % 3.86/4.04 do 0 intro. intros zenon_H78 zenon_H195 zenon_H1a4. % 3.86/4.04 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H198 | zenon_intro zenon_H199 ]. % 3.86/4.04 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((e2) = (op (op (e1) (e1)) (op (e1) (e1))))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H1a4. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H198. % 3.86/4.04 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H199]. % 3.86/4.04 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1a5]. % 3.86/4.04 congruence. % 3.86/4.04 cut (((op (e3) (e3)) = (e2)) = ((op (op (e1) (e1)) (op (e1) (e1))) = (e2))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H1a5. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H78. % 3.86/4.04 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 3.86/4.04 cut (((op (e3) (e3)) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H19b]. % 3.86/4.04 congruence. % 3.86/4.04 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H198 | zenon_intro zenon_H199 ]. % 3.86/4.04 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((op (e3) (e3)) = (op (op (e1) (e1)) (op (e1) (e1))))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H19b. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H198. % 3.86/4.04 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H199]. % 3.86/4.04 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H194]. % 3.86/4.04 congruence. % 3.86/4.04 apply (zenon_L144_); trivial. % 3.86/4.04 apply zenon_H199. apply refl_equal. % 3.86/4.04 apply zenon_H199. apply refl_equal. % 3.86/4.04 apply zenon_H4f. apply refl_equal. % 3.86/4.04 apply zenon_H199. apply refl_equal. % 3.86/4.04 apply zenon_H199. apply refl_equal. % 3.86/4.04 (* end of lemma zenon_L147_ *) % 3.86/4.04 assert (zenon_L148_ : ((op (e3) (e3)) = (e2)) -> ((op (e2) (e3)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> False). % 3.86/4.04 do 0 intro. intros zenon_H78 zenon_Hc3 zenon_H195. % 3.86/4.04 apply (zenon_notand_s _ _ ax18); [ zenon_intro zenon_H1a4 | zenon_intro zenon_H1a6 ]. % 3.86/4.04 apply (zenon_L147_); trivial. % 3.86/4.04 apply (zenon_notand_s _ _ zenon_H1a6); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H19d ]. % 3.86/4.04 elim (classic ((op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))))); [ zenon_intro zenon_H19f | zenon_intro zenon_H1a0 ]. % 3.86/4.04 cut (((op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) = ((e0) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H1a7. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H19f. % 3.86/4.04 cut (((op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1a0]. % 3.86/4.04 cut (((op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1a8]. % 3.86/4.04 congruence. % 3.86/4.04 cut (((op (e2) (e3)) = (e0)) = ((op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))) = (e0))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H1a8. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_Hc3. % 3.86/4.04 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H47]. % 3.86/4.04 cut (((op (e2) (e3)) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1a9]. % 3.86/4.04 congruence. % 3.86/4.04 elim (classic ((op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))))); [ zenon_intro zenon_H19f | zenon_intro zenon_H1a0 ]. % 3.86/4.04 cut (((op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) = ((op (e2) (e3)) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H1a9. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H19f. % 3.86/4.04 cut (((op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1a0]. % 3.86/4.04 cut (((op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1aa]. % 3.86/4.04 congruence. % 3.86/4.04 cut (((op (e1) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H196]. % 3.86/4.04 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1a5]. % 3.86/4.04 congruence. % 3.86/4.04 cut (((op (e3) (e3)) = (e2)) = ((op (op (e1) (e1)) (op (e1) (e1))) = (e2))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H1a5. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H78. % 3.86/4.04 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 3.86/4.04 cut (((op (e3) (e3)) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H19b]. % 3.86/4.04 congruence. % 3.86/4.04 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H198 | zenon_intro zenon_H199 ]. % 3.86/4.04 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((op (e3) (e3)) = (op (op (e1) (e1)) (op (e1) (e1))))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H19b. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H198. % 3.86/4.04 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H199]. % 3.86/4.04 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H194]. % 3.86/4.04 congruence. % 3.86/4.04 apply (zenon_L144_); trivial. % 3.86/4.04 apply zenon_H199. apply refl_equal. % 3.86/4.04 apply zenon_H199. apply refl_equal. % 3.86/4.04 apply zenon_H4f. apply refl_equal. % 3.86/4.04 exact (zenon_H196 zenon_H195). % 3.86/4.04 apply zenon_H1a0. apply refl_equal. % 3.86/4.04 apply zenon_H1a0. apply refl_equal. % 3.86/4.04 apply zenon_H47. apply refl_equal. % 3.86/4.04 apply zenon_H1a0. apply refl_equal. % 3.86/4.04 apply zenon_H1a0. apply refl_equal. % 3.86/4.04 apply zenon_H19d. apply sym_equal. exact zenon_H195. % 3.86/4.04 (* end of lemma zenon_L148_ *) % 3.86/4.04 assert (zenon_L149_ : ((op (e3) (e3)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (op (op (e0) (e0)) (op (e0) (e0))))) -> False). % 3.86/4.04 do 0 intro. intros zenon_H78 zenon_H66 zenon_H1ab. % 3.86/4.04 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H6c | zenon_intro zenon_H6d ]. % 3.86/4.04 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((e2) = (op (op (e0) (e0)) (op (e0) (e0))))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H1ab. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H6c. % 3.86/4.04 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 3.86/4.04 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1ac]. % 3.86/4.04 congruence. % 3.86/4.04 cut (((op (e3) (e3)) = (e2)) = ((op (op (e0) (e0)) (op (e0) (e0))) = (e2))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H1ac. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H78. % 3.86/4.04 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 3.86/4.04 cut (((op (e3) (e3)) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 3.86/4.04 congruence. % 3.86/4.04 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H6c | zenon_intro zenon_H6d ]. % 3.86/4.04 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((op (e3) (e3)) = (op (op (e0) (e0)) (op (e0) (e0))))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H6f. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H6c. % 3.86/4.04 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 3.86/4.04 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 3.86/4.04 congruence. % 3.86/4.04 apply (zenon_L21_); trivial. % 3.86/4.04 apply zenon_H6d. apply refl_equal. % 3.86/4.04 apply zenon_H6d. apply refl_equal. % 3.86/4.04 apply zenon_H4f. apply refl_equal. % 3.86/4.04 apply zenon_H6d. apply refl_equal. % 3.86/4.04 apply zenon_H6d. apply refl_equal. % 3.86/4.04 (* end of lemma zenon_L149_ *) % 3.86/4.04 assert (zenon_L150_ : ((op (e3) (e3)) = (e2)) -> ((op (e2) (e3)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> False). % 3.86/4.04 do 0 intro. intros zenon_H78 zenon_H8a zenon_H66. % 3.86/4.04 apply (zenon_notand_s _ _ ax20); [ zenon_intro zenon_H1ab | zenon_intro zenon_H1ad ]. % 3.86/4.04 apply (zenon_L149_); trivial. % 3.86/4.04 apply (zenon_notand_s _ _ zenon_H1ad); [ zenon_intro zenon_H1ae | zenon_intro zenon_H70 ]. % 3.86/4.04 elim (classic ((op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))))); [ zenon_intro zenon_H72 | zenon_intro zenon_H73 ]. % 3.86/4.04 cut (((op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) = ((e1) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H1ae. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H72. % 3.86/4.04 cut (((op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 3.86/4.04 cut (((op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1af]. % 3.86/4.04 congruence. % 3.86/4.04 cut (((op (e2) (e3)) = (e1)) = ((op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))) = (e1))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H1af. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H8a. % 3.86/4.04 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 3.86/4.04 cut (((op (e2) (e3)) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H1b0]. % 3.86/4.04 congruence. % 3.86/4.04 elim (classic ((op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))))); [ zenon_intro zenon_H72 | zenon_intro zenon_H73 ]. % 3.86/4.04 cut (((op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0)))) = ((op (e2) (e3)) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H1b0. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H72. % 3.86/4.04 cut (((op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))) = (op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 3.86/4.04 cut (((op (op (op (e0) (e0)) (op (e0) (e0))) (op (e0) (e0))) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1b1]. % 3.86/4.04 congruence. % 3.86/4.04 cut (((op (e0) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 3.86/4.04 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1ac]. % 3.86/4.04 congruence. % 3.86/4.04 cut (((op (e3) (e3)) = (e2)) = ((op (op (e0) (e0)) (op (e0) (e0))) = (e2))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H1ac. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H78. % 3.86/4.04 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 3.86/4.04 cut (((op (e3) (e3)) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 3.86/4.04 congruence. % 3.86/4.04 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H6c | zenon_intro zenon_H6d ]. % 3.86/4.04 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((op (e3) (e3)) = (op (op (e0) (e0)) (op (e0) (e0))))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H6f. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H6c. % 3.86/4.04 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 3.86/4.04 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 3.86/4.04 congruence. % 3.86/4.04 apply (zenon_L21_); trivial. % 3.86/4.04 apply zenon_H6d. apply refl_equal. % 3.86/4.04 apply zenon_H6d. apply refl_equal. % 3.86/4.04 apply zenon_H4f. apply refl_equal. % 3.86/4.04 exact (zenon_H67 zenon_H66). % 3.86/4.04 apply zenon_H73. apply refl_equal. % 3.86/4.04 apply zenon_H73. apply refl_equal. % 3.86/4.04 apply zenon_H4c. apply refl_equal. % 3.86/4.04 apply zenon_H73. apply refl_equal. % 3.86/4.04 apply zenon_H73. apply refl_equal. % 3.86/4.04 apply zenon_H70. apply sym_equal. exact zenon_H66. % 3.86/4.04 (* end of lemma zenon_L150_ *) % 3.86/4.04 assert (zenon_L151_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> False). % 3.86/4.04 do 0 intro. intros zenon_Hc2 zenon_Hca zenon_H12c. % 3.86/4.04 cut (((op (e0) (e3)) = (e3)) = ((op (e0) (e3)) = (op (e2) (e3)))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_Hc2. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_Hca. % 3.86/4.04 cut (((e3) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H12d]. % 3.86/4.04 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 3.86/4.04 congruence. % 3.86/4.04 apply zenon_Hc5. apply refl_equal. % 3.86/4.04 apply zenon_H12d. apply sym_equal. exact zenon_H12c. % 3.86/4.04 (* end of lemma zenon_L151_ *) % 3.86/4.04 assert (zenon_L152_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 3.86/4.04 do 0 intro. intros zenon_H1b2 zenon_H195 zenon_H66 zenon_H78 zenon_H91 zenon_Hc2 zenon_Hca. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H1b3 ]. % 3.86/4.04 apply (zenon_L148_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1b3); [ zenon_intro zenon_H8a | zenon_intro zenon_H1b4 ]. % 3.86/4.04 apply (zenon_L150_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H32 | zenon_intro zenon_H12c ]. % 3.86/4.04 exact (zenon_H91 zenon_H32). % 3.86/4.04 apply (zenon_L151_); trivial. % 3.86/4.04 (* end of lemma zenon_L152_ *) % 3.86/4.04 assert (zenon_L153_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e1) = (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) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 3.86/4.04 do 0 intro. intros zenon_H1b5 zenon_Hf2 zenon_Hc2 zenon_H91 zenon_H66 zenon_H1b2 zenon_H27 zenon_H50 zenon_H92 zenon_H9b zenon_H56 zenon_H153 zenon_He8 zenon_H17e zenon_H14b zenon_H182 zenon_H5c zenon_H183 zenon_H18c zenon_Hbc zenon_He9 zenon_H175 zenon_H4a zenon_H170 zenon_H18d zenon_H17b zenon_H18e zenon_H1b6 zenon_Hb3 zenon_H5d zenon_H156 zenon_Hca. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H179 | zenon_intro zenon_H1b7 ]. % 3.86/4.04 apply (zenon_L128_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1b7); [ zenon_intro zenon_H195 | zenon_intro zenon_H1b8 ]. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H15f | zenon_intro zenon_H1b9 ]. % 3.86/4.04 apply (zenon_L142_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1b9); [ zenon_intro zenon_H142 | zenon_intro zenon_H1ba ]. % 3.86/4.04 apply (zenon_L143_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1ba); [ zenon_intro zenon_H9c | zenon_intro zenon_Hda ]. % 3.86/4.04 apply (zenon_L31_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H60 | zenon_intro zenon_H95 ]. % 3.86/4.04 apply (zenon_L146_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H69 | zenon_intro zenon_H96 ]. % 3.86/4.04 apply (zenon_L132_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H32 | zenon_intro zenon_H78 ]. % 3.86/4.04 exact (zenon_H91 zenon_H32). % 3.86/4.04 apply (zenon_L152_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1b8); [ zenon_intro zenon_Hb2 | zenon_intro zenon_H12b ]. % 3.86/4.04 apply (zenon_L38_); trivial. % 3.86/4.04 apply (zenon_L103_); trivial. % 3.86/4.04 (* end of lemma zenon_L153_ *) % 3.86/4.04 assert (zenon_L154_ : (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> False). % 3.86/4.04 do 0 intro. intros zenon_H1bb zenon_H187 zenon_H5d. % 3.86/4.04 cut (((op (e3) (e0)) = (e3)) = ((op (e3) (e0)) = (op (e3) (e2)))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H1bb. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H187. % 3.86/4.04 cut (((e3) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H165]. % 3.86/4.04 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H160]. % 3.86/4.04 congruence. % 3.86/4.04 apply zenon_H160. apply refl_equal. % 3.86/4.04 apply zenon_H165. apply sym_equal. exact zenon_H5d. % 3.86/4.04 (* end of lemma zenon_L154_ *) % 3.86/4.04 assert (zenon_L155_ : (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> ((op (e3) (e0)) = (e1)) -> False). % 3.86/4.04 do 0 intro. intros zenon_H5c zenon_H187 zenon_H54. % 3.86/4.04 cut (((op (e3) (e0)) = (e3)) = ((e1) = (e3))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H5c. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H187. % 3.86/4.04 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H5b]. % 3.86/4.04 cut (((op (e3) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H189]. % 3.86/4.04 congruence. % 3.86/4.04 exact (zenon_H189 zenon_H54). % 3.86/4.04 apply zenon_H5b. apply refl_equal. % 3.86/4.04 (* end of lemma zenon_L155_ *) % 3.86/4.04 assert (zenon_L156_ : ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (e1))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e1)) -> False). % 3.86/4.04 do 0 intro. intros zenon_Hca zenon_H156 zenon_H5d zenon_Hb3 zenon_H1b6 zenon_H18e zenon_H17b zenon_H18d zenon_H4a zenon_H175 zenon_He9 zenon_Hbc zenon_H18c zenon_H183 zenon_H182 zenon_H14b zenon_He8 zenon_H153 zenon_H56 zenon_H92 zenon_H50 zenon_H27 zenon_H1b2 zenon_H91 zenon_Hc2 zenon_H1b5 zenon_H9b zenon_Hf2 zenon_H17e zenon_H170 zenon_H5c zenon_H54. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H66 | zenon_intro zenon_H18f ]. % 3.86/4.04 apply (zenon_L153_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H179 | zenon_intro zenon_H190 ]. % 3.86/4.04 apply (zenon_L128_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H187 ]. % 3.86/4.04 apply (zenon_L136_); trivial. % 3.86/4.04 apply (zenon_L155_); trivial. % 3.86/4.04 (* end of lemma zenon_L156_ *) % 3.86/4.04 assert (zenon_L157_ : ((op (e1) (e3)) = (e1)) -> ((op (e1) (e3)) = (e3)) -> (~((e1) = (e3))) -> False). % 3.86/4.04 do 0 intro. intros zenon_H27 zenon_H12b zenon_H5c. % 3.86/4.04 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H5b ]. % 3.86/4.04 cut (((e3) = (e3)) = ((e1) = (e3))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H5c. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_Hc7. % 3.86/4.04 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H5b]. % 3.86/4.04 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hc8]. % 3.86/4.04 congruence. % 3.86/4.04 cut (((op (e1) (e3)) = (e1)) = ((e3) = (e1))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_Hc8. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H27. % 3.86/4.04 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 3.86/4.04 cut (((op (e1) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1bc]. % 3.86/4.04 congruence. % 3.86/4.04 exact (zenon_H1bc zenon_H12b). % 3.86/4.04 apply zenon_H4c. apply refl_equal. % 3.86/4.04 apply zenon_H5b. apply refl_equal. % 3.86/4.04 apply zenon_H5b. apply refl_equal. % 3.86/4.04 (* end of lemma zenon_L157_ *) % 3.86/4.04 assert (zenon_L158_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> ((op (e3) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 3.86/4.04 do 0 intro. intros zenon_H158 zenon_H153 zenon_H16d zenon_H156 zenon_H27 zenon_H195 zenon_Hda zenon_Hc2 zenon_H12c. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H22 | zenon_intro zenon_H159 ]. % 3.86/4.04 apply (zenon_L119_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H159); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H15a ]. % 3.86/4.04 apply (zenon_L141_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_H60 | zenon_intro zenon_Hca ]. % 3.86/4.04 apply (zenon_L146_); trivial. % 3.86/4.04 apply (zenon_L151_); trivial. % 3.86/4.04 (* end of lemma zenon_L158_ *) % 3.86/4.04 assert (zenon_L159_ : (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (e1))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 3.86/4.04 do 0 intro. intros zenon_Hdc zenon_H158 zenon_H153 zenon_H16d zenon_H156 zenon_Hc2 zenon_H1b6 zenon_H18e zenon_H17b zenon_H18d zenon_H4a zenon_H175 zenon_He9 zenon_Hbc zenon_H18c zenon_H183 zenon_H182 zenon_H14b zenon_He8 zenon_H56 zenon_H92 zenon_H50 zenon_H1b2 zenon_H91 zenon_H1b5 zenon_H9b zenon_Hf2 zenon_H17e zenon_H170 zenon_H54 zenon_H1bd zenon_Hb3 zenon_H5d zenon_H27 zenon_H5c. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H179 | zenon_intro zenon_H1b7 ]. % 3.86/4.04 apply (zenon_L128_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1b7); [ zenon_intro zenon_H195 | zenon_intro zenon_H1b8 ]. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H15f | zenon_intro zenon_H1b9 ]. % 3.86/4.04 apply (zenon_L142_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1b9); [ zenon_intro zenon_H142 | zenon_intro zenon_H1ba ]. % 3.86/4.04 apply (zenon_L143_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1ba); [ zenon_intro zenon_H9c | zenon_intro zenon_Hda ]. % 3.86/4.04 apply (zenon_L31_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1bd); [ zenon_intro zenon_Hca | zenon_intro zenon_H1be ]. % 3.86/4.04 apply (zenon_L156_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1be); [ zenon_intro zenon_H12b | zenon_intro zenon_H1bf ]. % 3.86/4.04 apply (zenon_L157_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1bf); [ zenon_intro zenon_H12c | zenon_intro zenon_H39 ]. % 3.86/4.04 apply (zenon_L158_); trivial. % 3.86/4.04 apply (zenon_L51_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1b8); [ zenon_intro zenon_Hb2 | zenon_intro zenon_H12b ]. % 3.86/4.04 apply (zenon_L38_); trivial. % 3.86/4.04 apply (zenon_L157_); trivial. % 3.86/4.04 (* end of lemma zenon_L159_ *) % 3.86/4.04 assert (zenon_L160_ : (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (e0)) = (e0)) -> False). % 3.86/4.04 do 0 intro. intros zenon_H61 zenon_H170 zenon_H48. % 3.86/4.04 cut (((op (e2) (e0)) = (e2)) = ((e0) = (e2))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H61. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H170. % 3.86/4.04 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 3.86/4.04 cut (((op (e2) (e0)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1c0]. % 3.86/4.04 congruence. % 3.86/4.04 exact (zenon_H1c0 zenon_H48). % 3.86/4.04 apply zenon_H4f. apply refl_equal. % 3.86/4.04 (* end of lemma zenon_L160_ *) % 3.86/4.04 assert (zenon_L161_ : ((op (e2) (e0)) = (e2)) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> False). % 3.86/4.04 do 0 intro. intros zenon_H170 zenon_Hfe zenon_H1c1. % 3.86/4.04 elim (classic ((op (e2) (e0)) = (op (e2) (e0)))); [ zenon_intro zenon_H132 | zenon_intro zenon_H9a ]. % 3.86/4.04 cut (((op (e2) (e0)) = (op (e2) (e0))) = ((op (e0) (e0)) = (op (e2) (e0)))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H1c1. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H132. % 3.86/4.04 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 3.86/4.04 cut (((op (e2) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1c2]. % 3.86/4.04 congruence. % 3.86/4.04 cut (((op (e2) (e0)) = (e2)) = ((op (e2) (e0)) = (op (e0) (e0)))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H1c2. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H170. % 3.86/4.04 cut (((e2) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H102]. % 3.86/4.04 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 3.86/4.04 congruence. % 3.86/4.04 apply zenon_H9a. apply refl_equal. % 3.86/4.04 apply zenon_H102. apply sym_equal. exact zenon_Hfe. % 3.86/4.04 apply zenon_H9a. apply refl_equal. % 3.86/4.04 apply zenon_H9a. apply refl_equal. % 3.86/4.04 (* end of lemma zenon_L161_ *) % 3.86/4.04 assert (zenon_L162_ : (~((e1) = (e3))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e1)) = (e1)) -> False). % 3.86/4.04 do 0 intro. intros zenon_H5c zenon_Hf6 zenon_H58. % 3.86/4.04 cut (((op (e3) (e1)) = (e3)) = ((e1) = (e3))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H5c. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_Hf6. % 3.86/4.04 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H5b]. % 3.86/4.04 cut (((op (e3) (e1)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1c3]. % 3.86/4.04 congruence. % 3.86/4.04 exact (zenon_H1c3 zenon_H58). % 3.86/4.04 apply zenon_H5b. apply refl_equal. % 3.86/4.04 (* end of lemma zenon_L162_ *) % 3.86/4.04 assert (zenon_L163_ : (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> False). % 3.86/4.04 do 0 intro. intros zenon_Hb3 zenon_H3d zenon_H5e. % 3.86/4.04 cut (((op (e1) (e2)) = (e1)) = ((op (e1) (e2)) = (op (e3) (e2)))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_Hb3. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H3d. % 3.86/4.04 cut (((e1) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1c4]. % 3.86/4.04 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Had]. % 3.86/4.04 congruence. % 3.86/4.04 apply zenon_Had. apply refl_equal. % 3.86/4.04 apply zenon_H1c4. apply sym_equal. exact zenon_H5e. % 3.86/4.04 (* end of lemma zenon_L163_ *) % 3.86/4.04 assert (zenon_L164_ : ((op (e1) (e2)) = (e1)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> False). % 3.86/4.04 do 0 intro. intros zenon_H3d zenon_Ha4 zenon_Hae. % 3.86/4.04 elim (classic ((op (e1) (e2)) = (op (e1) (e2)))); [ zenon_intro zenon_H162 | zenon_intro zenon_Had ]. % 3.86/4.04 cut (((op (e1) (e2)) = (op (e1) (e2))) = ((op (e0) (e2)) = (op (e1) (e2)))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_Hae. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H162. % 3.86/4.04 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Had]. % 3.86/4.04 cut (((op (e1) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1c5]. % 3.86/4.04 congruence. % 3.86/4.04 cut (((op (e1) (e2)) = (e1)) = ((op (e1) (e2)) = (op (e0) (e2)))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H1c5. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H3d. % 3.86/4.04 cut (((e1) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1c6]. % 3.86/4.04 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Had]. % 3.86/4.04 congruence. % 3.86/4.04 apply zenon_Had. apply refl_equal. % 3.86/4.04 apply zenon_H1c6. apply sym_equal. exact zenon_Ha4. % 3.86/4.04 apply zenon_Had. apply refl_equal. % 3.86/4.04 apply zenon_Had. apply refl_equal. % 3.86/4.04 (* end of lemma zenon_L164_ *) % 3.86/4.04 assert (zenon_L165_ : (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> False). % 3.86/4.04 do 0 intro. intros zenon_H1bb zenon_H15f zenon_H9c. % 3.86/4.04 cut (((op (e3) (e0)) = (e0)) = ((op (e3) (e0)) = (op (e3) (e2)))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H1bb. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H15f. % 3.86/4.04 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1c7]. % 3.86/4.04 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H160]. % 3.86/4.04 congruence. % 3.86/4.04 apply zenon_H160. apply refl_equal. % 3.86/4.04 apply zenon_H1c7. apply sym_equal. exact zenon_H9c. % 3.86/4.04 (* end of lemma zenon_L165_ *) % 3.86/4.04 assert (zenon_L166_ : (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e3) (e2)) = (e2)) -> False). % 3.86/4.04 do 0 intro. intros zenon_Hbc zenon_Haf zenon_H1c8. % 3.86/4.04 cut (((op (e0) (e2)) = (e2)) = ((op (e0) (e2)) = (op (e3) (e2)))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_Hbc. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_Haf. % 3.86/4.04 cut (((e2) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1c9]. % 3.86/4.04 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H24]. % 3.86/4.04 congruence. % 3.86/4.04 apply zenon_H24. apply refl_equal. % 3.86/4.04 apply zenon_H1c9. apply sym_equal. exact zenon_H1c8. % 3.86/4.04 (* end of lemma zenon_L166_ *) % 3.86/4.04 assert (zenon_L167_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> False). % 3.86/4.04 do 0 intro. intros zenon_H1ca zenon_H15f zenon_H1bb zenon_H3d zenon_Hb3 zenon_Haf zenon_Hbc zenon_H164 zenon_Hf6. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_H9c | zenon_intro zenon_H1cb ]. % 3.86/4.04 apply (zenon_L165_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H5e | zenon_intro zenon_H1cc ]. % 3.86/4.04 apply (zenon_L163_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H5d ]. % 3.86/4.04 apply (zenon_L166_); trivial. % 3.86/4.04 apply (zenon_L115_); trivial. % 3.86/4.04 (* end of lemma zenon_L167_ *) % 3.86/4.04 assert (zenon_L168_ : (~((op (op (e1) (e1)) (op (e1) (e1))) = (op (e2) (e2)))) -> ((op (e1) (e1)) = (e2)) -> False). % 3.86/4.04 do 0 intro. intros zenon_H1cd zenon_H1ce. % 3.86/4.04 cut (((op (e1) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1cf]. % 3.86/4.04 cut (((op (e1) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1cf]. % 3.86/4.04 congruence. % 3.86/4.04 exact (zenon_H1cf zenon_H1ce). % 3.86/4.04 exact (zenon_H1cf zenon_H1ce). % 3.86/4.04 (* end of lemma zenon_L168_ *) % 3.86/4.04 assert (zenon_L169_ : ((op (e2) (e2)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> (~((e0) = (op (op (e1) (e1)) (op (e1) (e1))))) -> False). % 3.86/4.04 do 0 intro. intros zenon_H98 zenon_H1ce zenon_H197. % 3.86/4.04 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H198 | zenon_intro zenon_H199 ]. % 3.86/4.04 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((e0) = (op (op (e1) (e1)) (op (e1) (e1))))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H197. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H198. % 3.86/4.04 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H199]. % 3.86/4.04 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H19a]. % 3.86/4.04 congruence. % 3.86/4.04 cut (((op (e2) (e2)) = (e0)) = ((op (op (e1) (e1)) (op (e1) (e1))) = (e0))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H19a. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H98. % 3.86/4.04 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H47]. % 3.86/4.04 cut (((op (e2) (e2)) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1d0]. % 3.86/4.04 congruence. % 3.86/4.04 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H198 | zenon_intro zenon_H199 ]. % 3.86/4.04 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((op (e2) (e2)) = (op (op (e1) (e1)) (op (e1) (e1))))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H1d0. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H198. % 3.86/4.04 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H199]. % 3.86/4.04 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1cd]. % 3.86/4.04 congruence. % 3.86/4.04 apply (zenon_L168_); trivial. % 3.86/4.04 apply zenon_H199. apply refl_equal. % 3.86/4.04 apply zenon_H199. apply refl_equal. % 3.86/4.04 apply zenon_H47. apply refl_equal. % 3.86/4.04 apply zenon_H199. apply refl_equal. % 3.86/4.04 apply zenon_H199. apply refl_equal. % 3.86/4.04 (* end of lemma zenon_L169_ *) % 3.86/4.04 assert (zenon_L170_ : ((op (e2) (e2)) = (e0)) -> ((op (e0) (e2)) = (e3)) -> ((op (e1) (e1)) = (e2)) -> False). % 3.86/4.04 do 0 intro. intros zenon_H98 zenon_Hbb zenon_H1ce. % 3.86/4.04 apply (zenon_notand_s _ _ ax10); [ zenon_intro zenon_H197 | zenon_intro zenon_H1d1 ]. % 3.86/4.04 apply (zenon_L169_); trivial. % 3.86/4.04 apply (zenon_notand_s _ _ zenon_H1d1); [ zenon_intro zenon_H1d3 | zenon_intro zenon_H1d2 ]. % 3.86/4.04 elim (classic ((op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))))); [ zenon_intro zenon_H19f | zenon_intro zenon_H1a0 ]. % 3.86/4.04 cut (((op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) = ((e3) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H1d3. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H19f. % 3.86/4.04 cut (((op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1a0]. % 3.86/4.04 cut (((op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1d4]. % 3.86/4.04 congruence. % 3.86/4.04 cut (((op (e0) (e2)) = (e3)) = ((op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))) = (e3))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H1d4. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_Hbb. % 3.86/4.04 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H5b]. % 3.86/4.04 cut (((op (e0) (e2)) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1d5]. % 3.86/4.04 congruence. % 3.86/4.04 elim (classic ((op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))))); [ zenon_intro zenon_H19f | zenon_intro zenon_H1a0 ]. % 3.86/4.04 cut (((op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1)))) = ((op (e0) (e2)) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H1d5. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H19f. % 3.86/4.04 cut (((op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))) = (op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1a0]. % 3.86/4.04 cut (((op (op (op (e1) (e1)) (op (e1) (e1))) (op (e1) (e1))) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1d6]. % 3.86/4.04 congruence. % 3.86/4.04 cut (((op (e1) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1cf]. % 3.86/4.04 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H19a]. % 3.86/4.04 congruence. % 3.86/4.04 cut (((op (e2) (e2)) = (e0)) = ((op (op (e1) (e1)) (op (e1) (e1))) = (e0))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H19a. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H98. % 3.86/4.04 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H47]. % 3.86/4.04 cut (((op (e2) (e2)) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1d0]. % 3.86/4.04 congruence. % 3.86/4.04 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H198 | zenon_intro zenon_H199 ]. % 3.86/4.04 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((op (e2) (e2)) = (op (op (e1) (e1)) (op (e1) (e1))))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H1d0. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H198. % 3.86/4.04 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H199]. % 3.86/4.04 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1cd]. % 3.86/4.04 congruence. % 3.86/4.04 apply (zenon_L168_); trivial. % 3.86/4.04 apply zenon_H199. apply refl_equal. % 3.86/4.04 apply zenon_H199. apply refl_equal. % 3.86/4.04 apply zenon_H47. apply refl_equal. % 3.86/4.04 exact (zenon_H1cf zenon_H1ce). % 3.86/4.04 apply zenon_H1a0. apply refl_equal. % 3.86/4.04 apply zenon_H1a0. apply refl_equal. % 3.86/4.04 apply zenon_H5b. apply refl_equal. % 3.86/4.04 apply zenon_H1a0. apply refl_equal. % 3.86/4.04 apply zenon_H1a0. apply refl_equal. % 3.86/4.04 apply zenon_H1d2. apply sym_equal. exact zenon_H1ce. % 3.86/4.04 (* end of lemma zenon_L170_ *) % 3.86/4.04 assert (zenon_L171_ : ((op (e3) (e1)) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 3.86/4.04 do 0 intro. intros zenon_Hf6 zenon_H195 zenon_H1d7. % 3.86/4.04 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_Hf9 | zenon_intro zenon_He2 ]. % 3.86/4.04 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e1) (e1)) = (op (e3) (e1)))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H1d7. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_Hf9. % 3.86/4.04 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_He2]. % 3.86/4.04 cut (((op (e3) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1d8]. % 3.86/4.04 congruence. % 3.86/4.04 cut (((op (e3) (e1)) = (e3)) = ((op (e3) (e1)) = (op (e1) (e1)))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H1d8. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_Hf6. % 3.86/4.04 cut (((e3) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H19d]. % 3.86/4.04 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_He2]. % 3.86/4.04 congruence. % 3.86/4.04 apply zenon_He2. apply refl_equal. % 3.86/4.04 apply zenon_H19d. apply sym_equal. exact zenon_H195. % 3.86/4.04 apply zenon_He2. apply refl_equal. % 3.86/4.04 apply zenon_He2. apply refl_equal. % 3.86/4.04 (* end of lemma zenon_L171_ *) % 3.86/4.04 assert (zenon_L172_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e0) (e2)) = (e3)) -> ((op (e2) (e2)) = (e0)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 3.86/4.04 do 0 intro. intros zenon_H1d9 zenon_H68 zenon_H139 zenon_H1da zenon_H3d zenon_Hbb zenon_H98 zenon_Hf6 zenon_H1d7. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_H137 | zenon_intro zenon_H1db ]. % 3.86/4.04 apply (zenon_L90_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1db); [ zenon_intro zenon_H1f | zenon_intro zenon_H1dc ]. % 3.86/4.04 elim (classic ((op (e1) (e2)) = (op (e1) (e2)))); [ zenon_intro zenon_H162 | zenon_intro zenon_Had ]. % 3.86/4.04 cut (((op (e1) (e2)) = (op (e1) (e2))) = ((op (e1) (e1)) = (op (e1) (e2)))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H1da. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H162. % 3.86/4.04 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Had]. % 3.86/4.04 cut (((op (e1) (e2)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1dd]. % 3.86/4.04 congruence. % 3.86/4.04 cut (((op (e1) (e2)) = (e1)) = ((op (e1) (e2)) = (op (e1) (e1)))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H1dd. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H3d. % 3.86/4.04 cut (((e1) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_He7]. % 3.86/4.04 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Had]. % 3.86/4.04 congruence. % 3.86/4.04 apply zenon_Had. apply refl_equal. % 3.86/4.04 apply zenon_He7. apply sym_equal. exact zenon_H1f. % 3.86/4.04 apply zenon_Had. apply refl_equal. % 3.86/4.04 apply zenon_Had. apply refl_equal. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1dc); [ zenon_intro zenon_H1ce | zenon_intro zenon_H195 ]. % 3.86/4.04 apply (zenon_L170_); trivial. % 3.86/4.04 apply (zenon_L171_); trivial. % 3.86/4.04 (* end of lemma zenon_L172_ *) % 3.86/4.04 assert (zenon_L173_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> False). % 3.86/4.04 do 0 intro. intros zenon_H9e zenon_H1d7 zenon_Hf6 zenon_H3d zenon_H1da zenon_H139 zenon_H1d9 zenon_H1ca zenon_Hb3 zenon_Hbc zenon_H164 zenon_Hae zenon_H1de zenon_Hbf zenon_H5c zenon_H4a zenon_H8d zenon_H1bb zenon_H15f. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H9e); [ zenon_intro zenon_H21 | zenon_intro zenon_H9f ]. % 3.86/4.04 exact (zenon_H1de zenon_H21). % 3.86/4.04 apply (zenon_or_s _ _ zenon_H9f); [ zenon_intro zenon_H80 | zenon_intro zenon_Ha0 ]. % 3.86/4.04 apply (zenon_L130_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_Ha0); [ zenon_intro zenon_H98 | zenon_intro zenon_H9c ]. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H54 | zenon_intro zenon_H8e ]. % 3.86/4.04 apply (zenon_L140_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H58 | zenon_intro zenon_H8f ]. % 3.86/4.04 apply (zenon_L162_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H5e | zenon_intro zenon_H68 ]. % 3.86/4.04 apply (zenon_L163_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_H21 | zenon_intro zenon_Hc0 ]. % 3.86/4.04 exact (zenon_H1de zenon_H21). % 3.86/4.04 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Ha4 | zenon_intro zenon_Hc1 ]. % 3.86/4.04 apply (zenon_L164_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_Haf | zenon_intro zenon_Hbb ]. % 3.86/4.04 apply (zenon_L167_); trivial. % 3.86/4.04 apply (zenon_L172_); trivial. % 3.86/4.04 apply (zenon_L165_); trivial. % 3.86/4.04 (* end of lemma zenon_L173_ *) % 3.86/4.04 assert (zenon_L174_ : (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e3) (e0)) = (e2)) -> False). % 3.86/4.04 do 0 intro. intros zenon_H1df zenon_H170 zenon_H1e0. % 3.86/4.04 cut (((op (e2) (e0)) = (e2)) = ((op (e2) (e0)) = (op (e3) (e0)))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H1df. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H170. % 3.86/4.04 cut (((e2) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1e1]. % 3.86/4.04 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 3.86/4.04 congruence. % 3.86/4.04 apply zenon_H9a. apply refl_equal. % 3.86/4.04 apply zenon_H1e1. apply sym_equal. exact zenon_H1e0. % 3.86/4.04 (* end of lemma zenon_L174_ *) % 3.86/4.04 assert (zenon_L175_ : (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e1)) = (e2)) -> False). % 3.86/4.04 do 0 intro. intros zenon_H17e zenon_Hf6 zenon_H1e2. % 3.86/4.04 cut (((op (e3) (e1)) = (e3)) = ((e2) = (e3))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H17e. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_Hf6. % 3.86/4.04 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H5b]. % 3.86/4.04 cut (((op (e3) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1e3]. % 3.86/4.04 congruence. % 3.86/4.04 exact (zenon_H1e3 zenon_H1e2). % 3.86/4.04 apply zenon_H5b. apply refl_equal. % 3.86/4.04 (* end of lemma zenon_L175_ *) % 3.86/4.04 assert (zenon_L176_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> False). % 3.86/4.04 do 0 intro. intros zenon_H1e4 zenon_H170 zenon_H1df zenon_Hf6 zenon_H17e zenon_Haf zenon_Hbc zenon_H8a zenon_H66. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H1e0 | zenon_intro zenon_H1e5 ]. % 3.86/4.04 apply (zenon_L174_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1e5); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H1e6 ]. % 3.86/4.04 apply (zenon_L175_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1e6); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H78 ]. % 3.86/4.04 apply (zenon_L166_); trivial. % 3.86/4.04 apply (zenon_L150_); trivial. % 3.86/4.04 (* end of lemma zenon_L176_ *) % 3.86/4.04 assert (zenon_L177_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 3.86/4.04 do 0 intro. intros zenon_H1b2 zenon_H22 zenon_Hc2 zenon_H66 zenon_H78 zenon_H89 zenon_H128 zenon_H12b. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H1b3 ]. % 3.86/4.04 apply (zenon_L42_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1b3); [ zenon_intro zenon_H8a | zenon_intro zenon_H1b4 ]. % 3.86/4.04 apply (zenon_L150_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H32 | zenon_intro zenon_H12c ]. % 3.86/4.04 apply (zenon_L73_); trivial. % 3.86/4.04 apply (zenon_L82_); trivial. % 3.86/4.04 (* end of lemma zenon_L177_ *) % 3.86/4.04 assert (zenon_L178_ : (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e2)) -> ((op (e3) (e3)) = (e2)) -> False). % 3.86/4.04 do 0 intro. intros zenon_H10a zenon_H69 zenon_H78. % 3.86/4.04 cut (((op (e1) (e3)) = (e2)) = ((op (e1) (e3)) = (op (e3) (e3)))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H10a. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H69. % 3.86/4.04 cut (((e2) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 3.86/4.04 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 3.86/4.04 congruence. % 3.86/4.04 apply zenon_H2b. apply refl_equal. % 3.86/4.04 apply zenon_H82. apply sym_equal. exact zenon_H78. % 3.86/4.04 (* end of lemma zenon_L178_ *) % 3.86/4.04 assert (zenon_L179_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e3)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 3.86/4.04 do 0 intro. intros zenon_H1e4 zenon_H170 zenon_H1df zenon_Hf6 zenon_H17e zenon_Haf zenon_Hbc zenon_H12e zenon_Hd0 zenon_H68 zenon_Hf1 zenon_H10a zenon_H128 zenon_H12c. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H1e0 | zenon_intro zenon_H1e5 ]. % 3.86/4.04 apply (zenon_L174_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1e5); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H1e6 ]. % 3.86/4.04 apply (zenon_L175_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1e6); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H78 ]. % 3.86/4.04 apply (zenon_L166_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H10b | zenon_intro zenon_H12f ]. % 3.86/4.04 apply (zenon_L72_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H27 | zenon_intro zenon_H130 ]. % 3.86/4.04 exact (zenon_Hf1 zenon_H27). % 3.86/4.04 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H69 | zenon_intro zenon_H12b ]. % 3.86/4.04 apply (zenon_L178_); trivial. % 3.86/4.04 apply (zenon_L82_); trivial. % 3.86/4.04 (* end of lemma zenon_L179_ *) % 3.86/4.04 assert (zenon_L180_ : ((op (e0) (e2)) = (e2)) -> ((op (e0) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 3.86/4.04 do 0 intro. intros zenon_Haf zenon_Hbb zenon_H17e. % 3.86/4.04 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H5b ]. % 3.86/4.04 cut (((e3) = (e3)) = ((e2) = (e3))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H17e. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_Hc7. % 3.86/4.04 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H5b]. % 3.86/4.04 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H17f]. % 3.86/4.04 congruence. % 3.86/4.04 cut (((op (e0) (e2)) = (e2)) = ((e3) = (e2))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H17f. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_Haf. % 3.86/4.04 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 3.86/4.04 cut (((op (e0) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hfc]. % 3.86/4.04 congruence. % 3.86/4.04 exact (zenon_Hfc zenon_Hbb). % 3.86/4.04 apply zenon_H4f. apply refl_equal. % 3.86/4.04 apply zenon_H5b. apply refl_equal. % 3.86/4.04 apply zenon_H5b. apply refl_equal. % 3.86/4.04 (* end of lemma zenon_L180_ *) % 3.86/4.04 assert (zenon_L181_ : ((op (e1) (e2)) = (e1)) -> ((op (e1) (e2)) = (e3)) -> (~((e1) = (e3))) -> False). % 3.86/4.04 do 0 intro. intros zenon_H3d zenon_Hb2 zenon_H5c. % 3.86/4.04 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H5b ]. % 3.86/4.04 cut (((e3) = (e3)) = ((e1) = (e3))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H5c. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_Hc7. % 3.86/4.04 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H5b]. % 3.86/4.04 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hc8]. % 3.86/4.04 congruence. % 3.86/4.04 cut (((op (e1) (e2)) = (e1)) = ((e3) = (e1))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_Hc8. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H3d. % 3.86/4.04 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 3.86/4.04 cut (((op (e1) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1e7]. % 3.86/4.04 congruence. % 3.86/4.04 exact (zenon_H1e7 zenon_Hb2). % 3.86/4.04 apply zenon_H4c. apply refl_equal. % 3.86/4.04 apply zenon_H5b. apply refl_equal. % 3.86/4.04 apply zenon_H5b. apply refl_equal. % 3.86/4.04 (* end of lemma zenon_L181_ *) % 3.86/4.04 assert (zenon_L182_ : ((op (e3) (e1)) = (e3)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> False). % 3.86/4.04 do 0 intro. intros zenon_Hf6 zenon_Hc6 zenon_H56. % 3.86/4.04 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_Hf9 | zenon_intro zenon_He2 ]. % 3.86/4.04 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e0) (e1)) = (op (e3) (e1)))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H56. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_Hf9. % 3.86/4.04 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_He2]. % 3.86/4.04 cut (((op (e3) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1e8]. % 3.86/4.04 congruence. % 3.86/4.04 cut (((op (e3) (e1)) = (e3)) = ((op (e3) (e1)) = (op (e0) (e1)))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H1e8. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_Hf6. % 3.86/4.04 cut (((e3) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1e9]. % 3.86/4.04 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_He2]. % 3.86/4.04 congruence. % 3.86/4.04 apply zenon_He2. apply refl_equal. % 3.86/4.04 apply zenon_H1e9. apply sym_equal. exact zenon_Hc6. % 3.86/4.04 apply zenon_He2. apply refl_equal. % 3.86/4.04 apply zenon_He2. apply refl_equal. % 3.86/4.04 (* end of lemma zenon_L182_ *) % 3.86/4.04 assert (zenon_L183_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 3.86/4.04 do 0 intro. intros zenon_He9 zenon_H164 zenon_He3 zenon_H4a zenon_H1e4 zenon_H170 zenon_H1df zenon_Hbc zenon_H12e zenon_Hf1 zenon_H10a zenon_H128 zenon_H3d zenon_H5c zenon_H11a zenon_H1bd zenon_H89 zenon_Hc2 zenon_H1b2 zenon_He1 zenon_Hf8 zenon_H14a zenon_H56 zenon_Hf6 zenon_H17e zenon_Haf zenon_H22 zenon_H9b. % 3.86/4.04 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H66 | zenon_intro zenon_Hec ]. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H14d ]. % 3.86/4.04 apply (zenon_L136_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H14e ]. % 3.86/4.04 apply (zenon_L63_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H12c ]. % 3.86/4.04 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He4 ]. % 3.86/4.04 apply (zenon_L49_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H27 | zenon_intro zenon_He5 ]. % 3.86/4.04 exact (zenon_Hf1 zenon_H27). % 3.86/4.04 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_H8a | zenon_intro zenon_H68 ]. % 3.86/4.04 apply (zenon_L176_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H1e0 | zenon_intro zenon_H1e5 ]. % 3.86/4.04 apply (zenon_L174_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1e5); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H1e6 ]. % 3.86/4.04 apply (zenon_L175_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1e6); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H78 ]. % 3.86/4.04 apply (zenon_L166_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1bd); [ zenon_intro zenon_Hca | zenon_intro zenon_H1be ]. % 3.86/4.04 apply (zenon_L44_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1be); [ zenon_intro zenon_H12b | zenon_intro zenon_H1bf ]. % 3.86/4.04 apply (zenon_L177_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1bf); [ zenon_intro zenon_H12c | zenon_intro zenon_H39 ]. % 3.86/4.04 apply (zenon_L179_); trivial. % 3.86/4.04 apply (zenon_L74_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H11a); [ zenon_intro zenon_Hbb | zenon_intro zenon_H11b ]. % 3.86/4.04 apply (zenon_L180_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_Hb2 | zenon_intro zenon_H11c ]. % 3.86/4.04 apply (zenon_L181_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H5d ]. % 3.86/4.04 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He4 ]. % 3.86/4.04 apply (zenon_L49_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H27 | zenon_intro zenon_He5 ]. % 3.86/4.04 exact (zenon_Hf1 zenon_H27). % 3.86/4.04 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_H8a | zenon_intro zenon_H68 ]. % 3.86/4.04 apply (zenon_L176_); trivial. % 3.86/4.04 apply (zenon_L179_); trivial. % 3.86/4.04 apply (zenon_L115_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hed ]. % 3.86/4.04 apply (zenon_L182_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hca ]. % 3.86/4.04 apply (zenon_L180_); trivial. % 3.86/4.04 apply (zenon_L44_); trivial. % 3.86/4.04 (* end of lemma zenon_L183_ *) % 3.86/4.04 assert (zenon_L184_ : (((op (e0) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3)))) -> (~((op (e0) (e3)) = (e0))) -> False). % 3.86/4.04 do 0 intro. intros zenon_H25 zenon_H1ea. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H25). zenon_intro zenon_H22. zenon_intro zenon_H26. % 3.86/4.04 exact (zenon_H1ea zenon_H22). % 3.86/4.04 (* end of lemma zenon_L184_ *) % 3.86/4.04 assert (zenon_L185_ : ((op (e3) (e0)) = (e3)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> False). % 3.86/4.04 do 0 intro. intros zenon_H187 zenon_H66 zenon_H1eb. % 3.86/4.04 elim (classic ((op (e3) (e0)) = (op (e3) (e0)))); [ zenon_intro zenon_H1ec | zenon_intro zenon_H160 ]. % 3.86/4.04 cut (((op (e3) (e0)) = (op (e3) (e0))) = ((op (e0) (e0)) = (op (e3) (e0)))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H1eb. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H1ec. % 3.86/4.04 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H160]. % 3.86/4.04 cut (((op (e3) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1ed]. % 3.86/4.04 congruence. % 3.86/4.04 cut (((op (e3) (e0)) = (e3)) = ((op (e3) (e0)) = (op (e0) (e0)))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H1ed. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H187. % 3.86/4.04 cut (((e3) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H70]. % 3.86/4.04 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H160]. % 3.86/4.04 congruence. % 3.86/4.04 apply zenon_H160. apply refl_equal. % 3.86/4.04 apply zenon_H70. apply sym_equal. exact zenon_H66. % 3.86/4.04 apply zenon_H160. apply refl_equal. % 3.86/4.04 apply zenon_H160. apply refl_equal. % 3.86/4.04 (* end of lemma zenon_L185_ *) % 3.86/4.04 assert (zenon_L186_ : ((op (e1) (e0)) = (e0)) -> ((op (e1) (e0)) = (e2)) -> (~((e0) = (e2))) -> False). % 3.86/4.04 do 0 intro. intros zenon_Hf2 zenon_H1ee zenon_H61. % 3.86/4.04 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H62 | zenon_intro zenon_H4f ]. % 3.86/4.04 cut (((e2) = (e2)) = ((e0) = (e2))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H61. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H62. % 3.86/4.04 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 3.86/4.04 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H63]. % 3.86/4.04 congruence. % 3.86/4.04 cut (((op (e1) (e0)) = (e0)) = ((e2) = (e0))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H63. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_Hf2. % 3.86/4.04 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H47]. % 3.86/4.04 cut (((op (e1) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1ef]. % 3.86/4.04 congruence. % 3.86/4.04 exact (zenon_H1ef zenon_H1ee). % 3.86/4.04 apply zenon_H47. apply refl_equal. % 3.86/4.04 apply zenon_H4f. apply refl_equal. % 3.86/4.04 apply zenon_H4f. apply refl_equal. % 3.86/4.04 (* end of lemma zenon_L186_ *) % 3.86/4.04 assert (zenon_L187_ : (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (e1)) = (e0)) -> False). % 3.86/4.04 do 0 intro. intros zenon_H1f0 zenon_H153 zenon_Ha1. % 3.86/4.04 cut (((op (e0) (e1)) = (e0)) = ((op (e0) (e1)) = (op (e2) (e1)))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H1f0. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H153. % 3.86/4.04 cut (((e0) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H141]. % 3.86/4.04 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 3.86/4.04 congruence. % 3.86/4.04 apply zenon_H5a. apply refl_equal. % 3.86/4.04 apply zenon_H141. apply sym_equal. exact zenon_Ha1. % 3.86/4.04 (* end of lemma zenon_L187_ *) % 3.86/4.04 assert (zenon_L188_ : (((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 (e1) (e1)) = (e2)) -> ((op (e0) (e2)) = (e3)) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 3.86/4.04 do 0 intro. intros zenon_Hee zenon_H131 zenon_Hf2 zenon_H153 zenon_H1f0 zenon_H1ce zenon_Hbb zenon_H61 zenon_H32. % 3.86/4.04 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H48 | zenon_intro zenon_Hef ]. % 3.86/4.04 apply (zenon_L87_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_Hef); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hf0 ]. % 3.86/4.04 apply (zenon_L187_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H98 | zenon_intro zenon_Hc3 ]. % 3.86/4.04 apply (zenon_L170_); trivial. % 3.86/4.04 apply (zenon_L78_); trivial. % 3.86/4.04 (* end of lemma zenon_L188_ *) % 3.86/4.04 assert (zenon_L189_ : ((op (e1) (e2)) = (e1)) -> ((op (e1) (e2)) = (e2)) -> (~((e1) = (e2))) -> False). % 3.86/4.04 do 0 intro. intros zenon_H3d zenon_Hb0 zenon_H50. % 3.86/4.04 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H62 | zenon_intro zenon_H4f ]. % 3.86/4.04 cut (((e2) = (e2)) = ((e1) = (e2))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H50. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H62. % 3.86/4.04 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 3.86/4.04 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H15b]. % 3.86/4.04 congruence. % 3.86/4.04 cut (((op (e1) (e2)) = (e1)) = ((e2) = (e1))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H15b. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H3d. % 3.86/4.04 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 3.86/4.04 cut (((op (e1) (e2)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1f1]. % 3.86/4.04 congruence. % 3.86/4.04 exact (zenon_H1f1 zenon_Hb0). % 3.86/4.04 apply zenon_H4c. apply refl_equal. % 3.86/4.04 apply zenon_H4f. apply refl_equal. % 3.86/4.04 apply zenon_H4f. apply refl_equal. % 3.86/4.04 (* end of lemma zenon_L189_ *) % 3.86/4.04 assert (zenon_L190_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 3.86/4.04 do 0 intro. intros zenon_H1f2 zenon_H61 zenon_Hbb zenon_H1f0 zenon_H153 zenon_Hf2 zenon_H131 zenon_Hee zenon_H50 zenon_H3d zenon_H32 zenon_H128. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1f2); [ zenon_intro zenon_H1ee | zenon_intro zenon_H1f3 ]. % 3.86/4.04 apply (zenon_L186_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1f3); [ zenon_intro zenon_H1ce | zenon_intro zenon_H1f4 ]. % 3.86/4.04 apply (zenon_L188_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1f4); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H69 ]. % 3.86/4.04 apply (zenon_L189_); trivial. % 3.86/4.04 apply (zenon_L81_); trivial. % 3.86/4.04 (* end of lemma zenon_L190_ *) % 3.86/4.04 assert (zenon_L191_ : ((op (e0) (e3)) = (e1)) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e3))) -> False). % 3.86/4.04 do 0 intro. intros zenon_Hd7 zenon_Hca zenon_H5c. % 3.86/4.04 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H5b ]. % 3.86/4.04 cut (((e3) = (e3)) = ((e1) = (e3))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H5c. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_Hc7. % 3.86/4.04 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H5b]. % 3.86/4.04 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hc8]. % 3.86/4.04 congruence. % 3.86/4.04 cut (((op (e0) (e3)) = (e1)) = ((e3) = (e1))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_Hc8. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_Hd7. % 3.86/4.04 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 3.86/4.04 cut (((op (e0) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hcc]. % 3.86/4.04 congruence. % 3.86/4.04 exact (zenon_Hcc zenon_Hca). % 3.86/4.04 apply zenon_H4c. apply refl_equal. % 3.86/4.04 apply zenon_H5b. apply refl_equal. % 3.86/4.04 apply zenon_H5b. apply refl_equal. % 3.86/4.04 (* end of lemma zenon_L191_ *) % 3.86/4.04 assert (zenon_L192_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 3.86/4.04 do 0 intro. intros zenon_He3 zenon_H5c zenon_H3d zenon_H16e zenon_H50 zenon_H12e zenon_Hd0 zenon_H10a zenon_H128 zenon_H32 zenon_H156 zenon_Hca. % 3.86/4.04 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He4 ]. % 3.86/4.04 apply (zenon_L191_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H27 | zenon_intro zenon_He5 ]. % 3.86/4.04 apply (zenon_L121_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_H8a | zenon_intro zenon_H68 ]. % 3.86/4.04 apply (zenon_L100_); trivial. % 3.86/4.04 apply (zenon_L104_); trivial. % 3.86/4.04 (* end of lemma zenon_L192_ *) % 3.86/4.04 assert (zenon_L193_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (((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)))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 3.86/4.04 do 0 intro. intros zenon_H1f2 zenon_H36 zenon_He3 zenon_H5c zenon_H16e zenon_H12e zenon_H10a zenon_H156 zenon_Hca zenon_Hee zenon_H131 zenon_Hf2 zenon_H153 zenon_H1f0 zenon_H61 zenon_H11a zenon_H50 zenon_H3d zenon_H32 zenon_H128. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1f2); [ zenon_intro zenon_H1ee | zenon_intro zenon_H1f3 ]. % 3.86/4.04 apply (zenon_L186_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1f3); [ zenon_intro zenon_H1ce | zenon_intro zenon_H1f4 ]. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H11a); [ zenon_intro zenon_Hbb | zenon_intro zenon_H11b ]. % 3.86/4.04 apply (zenon_L188_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_Hb2 | zenon_intro zenon_H11c ]. % 3.86/4.04 apply (zenon_L181_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H5d ]. % 3.86/4.04 apply (zenon_L192_); trivial. % 3.86/4.04 exact (zenon_H36 zenon_H5d). % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1f4); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H69 ]. % 3.86/4.04 apply (zenon_L189_); trivial. % 3.86/4.04 apply (zenon_L81_); trivial. % 3.86/4.04 (* end of lemma zenon_L193_ *) % 3.86/4.04 assert (zenon_L194_ : ((op (e0) (e3)) = (e1)) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> False). % 3.86/4.04 do 0 intro. intros zenon_Hd7 zenon_H41 zenon_H1f5. % 3.86/4.04 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H1f6 | zenon_intro zenon_Hc5 ]. % 3.86/4.04 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (e0) (e0)) = (op (e0) (e3)))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H1f5. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H1f6. % 3.86/4.04 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 3.86/4.04 cut (((op (e0) (e3)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1f7]. % 3.86/4.04 congruence. % 3.86/4.04 cut (((op (e0) (e3)) = (e1)) = ((op (e0) (e3)) = (op (e0) (e0)))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H1f7. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_Hd7. % 3.86/4.04 cut (((e1) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 3.86/4.04 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 3.86/4.04 congruence. % 3.86/4.04 apply zenon_Hc5. apply refl_equal. % 3.86/4.04 apply zenon_H46. apply sym_equal. exact zenon_H41. % 3.86/4.04 apply zenon_Hc5. apply refl_equal. % 3.86/4.04 apply zenon_Hc5. apply refl_equal. % 3.86/4.04 (* end of lemma zenon_L194_ *) % 3.86/4.04 assert (zenon_L195_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e0)) = (e1))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 3.86/4.04 do 0 intro. intros zenon_H18e zenon_H1f5 zenon_Hd7 zenon_H18d zenon_H4a zenon_H48 zenon_H5c zenon_H187. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H41 | zenon_intro zenon_H191 ]. % 3.86/4.04 apply (zenon_L194_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_H28 | zenon_intro zenon_H192 ]. % 3.86/4.04 exact (zenon_H18d zenon_H28). % 3.86/4.04 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H49 | zenon_intro zenon_H54 ]. % 3.86/4.04 apply (zenon_L13_); trivial. % 3.86/4.04 apply (zenon_L155_); trivial. % 3.86/4.04 (* end of lemma zenon_L195_ *) % 3.86/4.04 assert (zenon_L196_ : (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (e2)) = (e1)) -> False). % 3.86/4.04 do 0 intro. intros zenon_Hac zenon_H3d zenon_H7a. % 3.86/4.04 cut (((op (e1) (e2)) = (e1)) = ((op (e1) (e2)) = (op (e2) (e2)))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_Hac. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H3d. % 3.86/4.04 cut (((e1) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hcd]. % 3.86/4.04 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Had]. % 3.86/4.04 congruence. % 3.86/4.04 apply zenon_Had. apply refl_equal. % 3.86/4.04 apply zenon_Hcd. apply sym_equal. exact zenon_H7a. % 3.86/4.04 (* end of lemma zenon_L196_ *) % 3.86/4.04 assert (zenon_L197_ : (((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)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> ((op (e1) (e3)) = (e0)) -> False). % 3.86/4.04 do 0 intro. intros zenon_Hd4 zenon_H48 zenon_H97 zenon_H3d zenon_Hac zenon_H107 zenon_H32 zenon_H68 zenon_H10b. % 3.86/4.04 apply (zenon_or_s _ _ zenon_Hd4); [ zenon_intro zenon_H98 | zenon_intro zenon_Hd5 ]. % 3.86/4.04 apply (zenon_L30_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_Hd5); [ zenon_intro zenon_H7a | zenon_intro zenon_Hd6 ]. % 3.86/4.04 apply (zenon_L196_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_Hd6); [ zenon_intro zenon_H40 | zenon_intro zenon_Hd0 ]. % 3.86/4.04 apply (zenon_L68_); trivial. % 3.86/4.04 apply (zenon_L72_); trivial. % 3.86/4.04 (* end of lemma zenon_L197_ *) % 3.86/4.04 assert (zenon_L198_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((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)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 3.86/4.04 do 0 intro. intros zenon_H12e zenon_H107 zenon_Hac zenon_H3d zenon_H97 zenon_H48 zenon_Hd4 zenon_H68 zenon_H10a zenon_H128 zenon_H32 zenon_H156 zenon_Hca. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H10b | zenon_intro zenon_H12f ]. % 3.86/4.04 apply (zenon_L197_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_H27 | zenon_intro zenon_H130 ]. % 3.86/4.04 apply (zenon_L102_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H69 | zenon_intro zenon_H12b ]. % 3.86/4.04 apply (zenon_L81_); trivial. % 3.86/4.04 apply (zenon_L103_); trivial. % 3.86/4.04 (* end of lemma zenon_L198_ *) % 3.86/4.04 assert (zenon_L199_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e0))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 3.86/4.04 do 0 intro. intros zenon_H158 zenon_H1ea zenon_H68 zenon_Hd9 zenon_Hc2 zenon_H32 zenon_H156 zenon_H12b. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H22 | zenon_intro zenon_H159 ]. % 3.86/4.04 exact (zenon_H1ea zenon_H22). % 3.86/4.04 apply (zenon_or_s _ _ zenon_H159); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H15a ]. % 3.86/4.04 apply (zenon_L101_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_H60 | zenon_intro zenon_Hca ]. % 3.86/4.04 apply (zenon_L98_); trivial. % 3.86/4.04 apply (zenon_L103_); trivial. % 3.86/4.04 (* end of lemma zenon_L199_ *) % 3.86/4.04 assert (zenon_L200_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e0))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 3.86/4.04 do 0 intro. intros zenon_H158 zenon_H1ea zenon_H68 zenon_Hd9 zenon_H32 zenon_Hc2 zenon_H12c. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H22 | zenon_intro zenon_H159 ]. % 3.86/4.04 exact (zenon_H1ea zenon_H22). % 3.86/4.04 apply (zenon_or_s _ _ zenon_H159); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H15a ]. % 3.86/4.04 apply (zenon_L101_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_H60 | zenon_intro zenon_Hca ]. % 3.86/4.04 apply (zenon_L98_); trivial. % 3.86/4.04 apply (zenon_L151_); trivial. % 3.86/4.04 (* end of lemma zenon_L200_ *) % 3.86/4.04 assert (zenon_L201_ : (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e3) (e3)) = (e3)) -> False). % 3.86/4.04 do 0 intro. intros zenon_H15e zenon_H187 zenon_H39. % 3.86/4.04 cut (((op (e3) (e0)) = (e3)) = ((op (e3) (e0)) = (op (e3) (e3)))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H15e. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H187. % 3.86/4.04 cut (((e3) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hdd]. % 3.86/4.04 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H160]. % 3.86/4.04 congruence. % 3.86/4.04 apply zenon_H160. apply refl_equal. % 3.86/4.04 apply zenon_Hdd. apply sym_equal. exact zenon_H39. % 3.86/4.04 (* end of lemma zenon_L201_ *) % 3.86/4.04 assert (zenon_L202_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((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)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e3)) -> False). % 3.86/4.04 do 0 intro. intros zenon_H1bd zenon_H128 zenon_H10a zenon_Hd4 zenon_H48 zenon_H97 zenon_H3d zenon_Hac zenon_H107 zenon_H12e zenon_H156 zenon_Hc2 zenon_H32 zenon_Hd9 zenon_H68 zenon_H1ea zenon_H158 zenon_H15e zenon_H187. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1bd); [ zenon_intro zenon_Hca | zenon_intro zenon_H1be ]. % 3.86/4.04 apply (zenon_L198_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1be); [ zenon_intro zenon_H12b | zenon_intro zenon_H1bf ]. % 3.86/4.04 apply (zenon_L199_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1bf); [ zenon_intro zenon_H12c | zenon_intro zenon_H39 ]. % 3.86/4.04 apply (zenon_L200_); trivial. % 3.86/4.04 apply (zenon_L201_); trivial. % 3.86/4.04 (* end of lemma zenon_L202_ *) % 3.86/4.04 assert (zenon_L203_ : (((op (e3) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 3.86/4.04 do 0 intro. intros zenon_H166 zenon_H187 zenon_H1bb. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H166). zenon_intro zenon_H5d. zenon_intro zenon_H91. % 3.86/4.04 apply (zenon_L154_); trivial. % 3.86/4.04 (* end of lemma zenon_L203_ *) % 3.86/4.04 assert (zenon_L204_ : (~((op (op (e2) (e2)) (op (e2) (e2))) = (op (e1) (e1)))) -> ((op (e2) (e2)) = (e1)) -> False). % 3.86/4.04 do 0 intro. intros zenon_H1f8 zenon_H7a. % 3.86/4.04 cut (((op (e2) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1f9]. % 3.86/4.04 cut (((op (e2) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1f9]. % 3.86/4.04 congruence. % 3.86/4.04 exact (zenon_H1f9 zenon_H7a). % 3.86/4.04 exact (zenon_H1f9 zenon_H7a). % 3.86/4.04 (* end of lemma zenon_L204_ *) % 3.86/4.04 assert (zenon_L205_ : ((op (e1) (e1)) = (e0)) -> ((op (e2) (e2)) = (e1)) -> (~((e0) = (op (op (e2) (e2)) (op (e2) (e2))))) -> False). % 3.86/4.04 do 0 intro. intros zenon_H137 zenon_H7a zenon_H11f. % 3.86/4.04 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H10f | zenon_intro zenon_H110 ]. % 3.86/4.04 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((e0) = (op (op (e2) (e2)) (op (e2) (e2))))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H11f. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H10f. % 3.86/4.04 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H110]. % 3.86/4.04 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H120]. % 3.86/4.04 congruence. % 3.86/4.04 cut (((op (e1) (e1)) = (e0)) = ((op (op (e2) (e2)) (op (e2) (e2))) = (e0))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H120. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H137. % 3.86/4.04 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H47]. % 3.86/4.04 cut (((op (e1) (e1)) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H1fa]. % 3.86/4.04 congruence. % 3.86/4.04 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H10f | zenon_intro zenon_H110 ]. % 3.86/4.04 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((op (e1) (e1)) = (op (op (e2) (e2)) (op (e2) (e2))))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H1fa. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H10f. % 3.86/4.04 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H110]. % 3.86/4.04 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1f8]. % 3.86/4.04 congruence. % 3.86/4.04 apply (zenon_L204_); trivial. % 3.86/4.04 apply zenon_H110. apply refl_equal. % 3.86/4.04 apply zenon_H110. apply refl_equal. % 3.86/4.04 apply zenon_H47. apply refl_equal. % 3.86/4.04 apply zenon_H110. apply refl_equal. % 3.86/4.04 apply zenon_H110. apply refl_equal. % 3.86/4.04 (* end of lemma zenon_L205_ *) % 3.86/4.04 assert (zenon_L206_ : ((op (e1) (e1)) = (e0)) -> ((op (e0) (e1)) = (e3)) -> ((op (e2) (e2)) = (e1)) -> False). % 3.86/4.04 do 0 intro. intros zenon_H137 zenon_Hc6 zenon_H7a. % 3.86/4.04 apply (zenon_notand_s _ _ ax11); [ zenon_intro zenon_H11f | zenon_intro zenon_H1fb ]. % 3.86/4.04 apply (zenon_L205_); trivial. % 3.86/4.04 apply (zenon_notand_s _ _ zenon_H1fb); [ zenon_intro zenon_H1fc | zenon_intro zenon_Hcd ]. % 3.86/4.04 elim (classic ((op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))))); [ zenon_intro zenon_H115 | zenon_intro zenon_H116 ]. % 3.86/4.04 cut (((op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) = ((e3) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H1fc. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H115. % 3.86/4.04 cut (((op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H116]. % 3.86/4.04 cut (((op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1fd]. % 3.86/4.04 congruence. % 3.86/4.04 cut (((op (e0) (e1)) = (e3)) = ((op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))) = (e3))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H1fd. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_Hc6. % 3.86/4.04 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H5b]. % 3.86/4.04 cut (((op (e0) (e1)) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H1fe]. % 3.86/4.04 congruence. % 3.86/4.04 elim (classic ((op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))))); [ zenon_intro zenon_H115 | zenon_intro zenon_H116 ]. % 3.86/4.04 cut (((op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2)))) = ((op (e0) (e1)) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H1fe. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H115. % 3.86/4.04 cut (((op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))) = (op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H116]. % 3.86/4.04 cut (((op (op (op (e2) (e2)) (op (e2) (e2))) (op (e2) (e2))) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1ff]. % 3.86/4.04 congruence. % 3.86/4.04 cut (((op (e2) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1f9]. % 3.86/4.04 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H120]. % 3.86/4.04 congruence. % 3.86/4.04 cut (((op (e1) (e1)) = (e0)) = ((op (op (e2) (e2)) (op (e2) (e2))) = (e0))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H120. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H137. % 3.86/4.04 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H47]. % 3.86/4.04 cut (((op (e1) (e1)) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H1fa]. % 3.86/4.04 congruence. % 3.86/4.04 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H10f | zenon_intro zenon_H110 ]. % 3.86/4.04 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((op (e1) (e1)) = (op (op (e2) (e2)) (op (e2) (e2))))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H1fa. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H10f. % 3.86/4.04 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H110]. % 3.86/4.04 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1f8]. % 3.86/4.04 congruence. % 3.86/4.04 apply (zenon_L204_); trivial. % 3.86/4.04 apply zenon_H110. apply refl_equal. % 3.86/4.04 apply zenon_H110. apply refl_equal. % 3.86/4.04 apply zenon_H47. apply refl_equal. % 3.86/4.04 exact (zenon_H1f9 zenon_H7a). % 3.86/4.04 apply zenon_H116. apply refl_equal. % 3.86/4.04 apply zenon_H116. apply refl_equal. % 3.86/4.04 apply zenon_H5b. apply refl_equal. % 3.86/4.04 apply zenon_H116. apply refl_equal. % 3.86/4.04 apply zenon_H116. apply refl_equal. % 3.86/4.04 apply zenon_Hcd. apply sym_equal. exact zenon_H7a. % 3.86/4.04 (* end of lemma zenon_L206_ *) % 3.86/4.04 assert (zenon_L207_ : (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e3)) = (e1)) -> False). % 3.86/4.04 do 0 intro. intros zenon_H128 zenon_H27 zenon_H8a. % 3.86/4.04 cut (((op (e1) (e3)) = (e1)) = ((op (e1) (e3)) = (op (e2) (e3)))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H128. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H27. % 3.86/4.04 cut (((e1) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H200]. % 3.86/4.04 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 3.86/4.04 congruence. % 3.86/4.04 apply zenon_H2b. apply refl_equal. % 3.86/4.04 apply zenon_H200. apply sym_equal. exact zenon_H8a. % 3.86/4.04 (* end of lemma zenon_L207_ *) % 3.86/4.04 assert (zenon_L208_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e3)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 3.86/4.04 do 0 intro. intros zenon_H90 zenon_H4a zenon_H48 zenon_H31 zenon_H50 zenon_Hc6 zenon_H137 zenon_H128 zenon_H27. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H49 | zenon_intro zenon_H93 ]. % 3.86/4.04 apply (zenon_L13_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H51 | zenon_intro zenon_H94 ]. % 3.86/4.04 apply (zenon_L15_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H7a | zenon_intro zenon_H8a ]. % 3.86/4.04 apply (zenon_L206_); trivial. % 3.86/4.04 apply (zenon_L207_); trivial. % 3.86/4.04 (* end of lemma zenon_L208_ *) % 3.86/4.04 assert (zenon_L209_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e3)) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> False). % 3.86/4.04 do 0 intro. intros zenon_H14b zenon_H131 zenon_H128 zenon_Hc6 zenon_H50 zenon_H31 zenon_H48 zenon_H90 zenon_H21 zenon_Hae zenon_H4a zenon_H27. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_Hf2 | zenon_intro zenon_H150 ]. % 3.86/4.04 apply (zenon_L87_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H137 | zenon_intro zenon_H151 ]. % 3.86/4.04 apply (zenon_L208_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H80 | zenon_intro zenon_H10b ]. % 3.86/4.04 apply (zenon_L94_); trivial. % 3.86/4.04 apply (zenon_L134_); trivial. % 3.86/4.04 (* end of lemma zenon_L209_ *) % 3.86/4.04 assert (zenon_L210_ : ((op (e3) (e0)) = (e3)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> False). % 3.86/4.04 do 0 intro. intros zenon_H187 zenon_Hf4 zenon_H1df. % 3.86/4.04 elim (classic ((op (e3) (e0)) = (op (e3) (e0)))); [ zenon_intro zenon_H1ec | zenon_intro zenon_H160 ]. % 3.86/4.04 cut (((op (e3) (e0)) = (op (e3) (e0))) = ((op (e2) (e0)) = (op (e3) (e0)))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H1df. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H1ec. % 3.86/4.04 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H160]. % 3.86/4.04 cut (((op (e3) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H201]. % 3.86/4.04 congruence. % 3.86/4.04 cut (((op (e3) (e0)) = (e3)) = ((op (e3) (e0)) = (op (e2) (e0)))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H201. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H187. % 3.86/4.04 cut (((e3) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H202]. % 3.86/4.04 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H160]. % 3.86/4.04 congruence. % 3.86/4.04 apply zenon_H160. apply refl_equal. % 3.86/4.04 apply zenon_H202. apply sym_equal. exact zenon_Hf4. % 3.86/4.04 apply zenon_H160. apply refl_equal. % 3.86/4.04 apply zenon_H160. apply refl_equal. % 3.86/4.04 (* end of lemma zenon_L210_ *) % 3.86/4.04 assert (zenon_L211_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (e2))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> False). % 3.86/4.04 do 0 intro. intros zenon_H203 zenon_H27 zenon_H4a zenon_Hae zenon_H21 zenon_H90 zenon_H31 zenon_H50 zenon_Hc6 zenon_H128 zenon_H131 zenon_H14b zenon_H41 zenon_H1c1 zenon_H16c zenon_H187 zenon_H1df. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H48 | zenon_intro zenon_H204 ]. % 3.86/4.04 apply (zenon_L209_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H49 | zenon_intro zenon_H205 ]. % 3.86/4.04 cut (((op (e0) (e0)) = (e1)) = ((op (e0) (e0)) = (op (e2) (e0)))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H1c1. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H41. % 3.86/4.04 cut (((e1) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H206]. % 3.86/4.04 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H207]. % 3.86/4.04 congruence. % 3.86/4.04 apply zenon_H207. apply refl_equal. % 3.86/4.04 apply zenon_H206. apply sym_equal. exact zenon_H49. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H205); [ zenon_intro zenon_H170 | zenon_intro zenon_Hf4 ]. % 3.86/4.04 exact (zenon_H16c zenon_H170). % 3.86/4.04 apply (zenon_L210_); trivial. % 3.86/4.04 (* end of lemma zenon_L211_ *) % 3.86/4.04 assert (zenon_L212_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 3.86/4.04 do 0 intro. intros zenon_H1b2 zenon_H195 zenon_H78 zenon_H27 zenon_H128 zenon_H31 zenon_H30 zenon_Hc2 zenon_Hca. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H1b3 ]. % 3.86/4.04 apply (zenon_L148_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1b3); [ zenon_intro zenon_H8a | zenon_intro zenon_H1b4 ]. % 3.86/4.04 apply (zenon_L207_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H32 | zenon_intro zenon_H12c ]. % 3.86/4.04 apply (zenon_L6_); trivial. % 3.86/4.04 apply (zenon_L151_); trivial. % 3.86/4.04 (* end of lemma zenon_L212_ *) % 3.86/4.04 assert (zenon_L213_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 3.86/4.04 do 0 intro. intros zenon_H92 zenon_H17e zenon_H50 zenon_H1b2 zenon_H195 zenon_H27 zenon_H128 zenon_H31 zenon_H30 zenon_Hc2 zenon_Hca. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H60 | zenon_intro zenon_H95 ]. % 3.86/4.04 apply (zenon_L131_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H69 | zenon_intro zenon_H96 ]. % 3.86/4.04 apply (zenon_L132_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H32 | zenon_intro zenon_H78 ]. % 3.86/4.04 apply (zenon_L6_); trivial. % 3.86/4.04 apply (zenon_L212_); trivial. % 3.86/4.04 (* end of lemma zenon_L213_ *) % 3.86/4.04 assert (zenon_L214_ : ((op (e2) (e1)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> (~((e2) = (e3))) -> False). % 3.86/4.04 do 0 intro. intros zenon_H31 zenon_Hf7 zenon_H17e. % 3.86/4.04 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H5b ]. % 3.86/4.04 cut (((e3) = (e3)) = ((e2) = (e3))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H17e. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_Hc7. % 3.86/4.04 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H5b]. % 3.86/4.04 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H17f]. % 3.86/4.04 congruence. % 3.86/4.04 cut (((op (e2) (e1)) = (e2)) = ((e3) = (e2))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H17f. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H31. % 3.86/4.04 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 3.86/4.04 cut (((op (e2) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H208]. % 3.86/4.04 congruence. % 3.86/4.04 exact (zenon_H208 zenon_Hf7). % 3.86/4.04 apply zenon_H4f. apply refl_equal. % 3.86/4.04 apply zenon_H5b. apply refl_equal. % 3.86/4.04 apply zenon_H5b. apply refl_equal. % 3.86/4.04 (* end of lemma zenon_L214_ *) % 3.86/4.04 assert (zenon_L215_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 3.86/4.04 do 0 intro. intros zenon_He9 zenon_H1eb zenon_H187 zenon_H5c zenon_H57 zenon_H9b zenon_H21 zenon_H60 zenon_H17e. % 3.86/4.04 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H66 | zenon_intro zenon_Hec ]. % 3.86/4.04 apply (zenon_L185_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hed ]. % 3.86/4.04 apply (zenon_L43_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hca ]. % 3.86/4.04 apply (zenon_L64_); trivial. % 3.86/4.04 apply (zenon_L131_); trivial. % 3.86/4.04 (* end of lemma zenon_L215_ *) % 3.86/4.04 assert (zenon_L216_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 3.86/4.04 do 0 intro. intros zenon_H92 zenon_H17e zenon_H21 zenon_H9b zenon_H57 zenon_H5c zenon_H187 zenon_H1eb zenon_He9 zenon_H50 zenon_H1b2 zenon_H195 zenon_H27 zenon_H128 zenon_H31 zenon_H30 zenon_Hc2 zenon_Hca. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H60 | zenon_intro zenon_H95 ]. % 3.86/4.04 apply (zenon_L215_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H69 | zenon_intro zenon_H96 ]. % 3.86/4.04 apply (zenon_L132_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H32 | zenon_intro zenon_H78 ]. % 3.86/4.04 apply (zenon_L6_); trivial. % 3.86/4.04 apply (zenon_L212_); trivial. % 3.86/4.04 (* end of lemma zenon_L216_ *) % 3.86/4.04 assert (zenon_L217_ : (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e3) (e1)) = (e3)) -> False). % 3.86/4.04 do 0 intro. intros zenon_H209 zenon_H187 zenon_Hf6. % 3.86/4.04 cut (((op (e3) (e0)) = (e3)) = ((op (e3) (e0)) = (op (e3) (e1)))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H209. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H187. % 3.86/4.04 cut (((e3) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H20a]. % 3.86/4.04 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H160]. % 3.86/4.04 congruence. % 3.86/4.04 apply zenon_H160. apply refl_equal. % 3.86/4.04 apply zenon_H20a. apply sym_equal. exact zenon_Hf6. % 3.86/4.04 (* end of lemma zenon_L217_ *) % 3.86/4.04 assert (zenon_L218_ : (((op (e3) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 3.86/4.04 do 0 intro. intros zenon_H20b zenon_H187 zenon_H209. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H20b). zenon_intro zenon_Hf6. zenon_intro zenon_Hf1. % 3.86/4.04 apply (zenon_L217_); trivial. % 3.86/4.04 (* end of lemma zenon_L218_ *) % 3.86/4.04 apply (zenon_and_s _ _ ax1). zenon_intro zenon_H20d. zenon_intro zenon_H20c. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H20c). zenon_intro zenon_H20f. zenon_intro zenon_H20e. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H20e). zenon_intro zenon_Hbf. zenon_intro zenon_H210. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H210). zenon_intro zenon_H158. zenon_intro zenon_H211. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H211). zenon_intro zenon_H213. zenon_intro zenon_H212. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H212). zenon_intro zenon_H1d9. zenon_intro zenon_H214. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H214). zenon_intro zenon_Hb8. zenon_intro zenon_H215. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H215). zenon_intro zenon_H12e. zenon_intro zenon_H216. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H216). zenon_intro zenon_H203. zenon_intro zenon_H217. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H217). zenon_intro zenon_H219. zenon_intro zenon_H218. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H218). zenon_intro zenon_Hd4. zenon_intro zenon_H21a. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H21a). zenon_intro zenon_H1b2. zenon_intro zenon_H21b. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H21b). zenon_intro zenon_H21d. zenon_intro zenon_H21c. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H21c). zenon_intro zenon_H21f. zenon_intro zenon_H21e. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H21e). zenon_intro zenon_H1ca. zenon_intro zenon_Hde. % 3.86/4.04 apply (zenon_and_s _ _ ax2). zenon_intro zenon_H221. zenon_intro zenon_H220. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H220). zenon_intro zenon_H223. zenon_intro zenon_H222. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H222). zenon_intro zenon_He8. zenon_intro zenon_H224. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H224). zenon_intro zenon_H18e. zenon_intro zenon_H225. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H225). zenon_intro zenon_H147. zenon_intro zenon_H226. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H226). zenon_intro zenon_H228. zenon_intro zenon_H227. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H227). zenon_intro zenon_He9. zenon_intro zenon_H229. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H229). zenon_intro zenon_H18c. zenon_intro zenon_H22a. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H22a). zenon_intro zenon_H14b. zenon_intro zenon_H22b. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H22b). zenon_intro zenon_H149. zenon_intro zenon_H22c. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H22c). zenon_intro zenon_H22e. zenon_intro zenon_H22d. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H22d). zenon_intro zenon_H230. zenon_intro zenon_H22f. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H22f). zenon_intro zenon_H1f2. zenon_intro zenon_H231. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H231). zenon_intro zenon_H233. zenon_intro zenon_H232. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H232). zenon_intro zenon_H1b5. zenon_intro zenon_H234. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H234). zenon_intro zenon_H236. zenon_intro zenon_H235. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H235). zenon_intro zenon_Hee. zenon_intro zenon_H237. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H237). zenon_intro zenon_H9e. zenon_intro zenon_H238. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H238). zenon_intro zenon_H90. zenon_intro zenon_H239. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H239). zenon_intro zenon_H183. zenon_intro zenon_H23a. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H23a). zenon_intro zenon_H23c. zenon_intro zenon_H23b. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H23b). zenon_intro zenon_H23e. zenon_intro zenon_H23d. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H23d). zenon_intro zenon_H14a. zenon_intro zenon_H23f. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H23f). zenon_intro zenon_H11a. zenon_intro zenon_H240. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H240). zenon_intro zenon_H1b6. zenon_intro zenon_H241. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H241). zenon_intro zenon_H125. zenon_intro zenon_H242. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H242). zenon_intro zenon_H8d. zenon_intro zenon_H243. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H243). zenon_intro zenon_He3. zenon_intro zenon_H244. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H244). zenon_intro zenon_H1e4. zenon_intro zenon_H245. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H245). zenon_intro zenon_H92. zenon_intro zenon_H246. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H246). zenon_intro zenon_H247. zenon_intro zenon_H1bd. % 3.86/4.04 apply (zenon_and_s _ _ ax3). zenon_intro zenon_H42. zenon_intro zenon_H248. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H248). zenon_intro zenon_H1c1. zenon_intro zenon_H249. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H249). zenon_intro zenon_H1eb. zenon_intro zenon_H24a. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H24a). zenon_intro zenon_H131. zenon_intro zenon_H24b. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H24b). zenon_intro zenon_H53. zenon_intro zenon_H24c. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H24c). zenon_intro zenon_H1df. zenon_intro zenon_H24d. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H24d). zenon_intro zenon_H182. zenon_intro zenon_H24e. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H24e). zenon_intro zenon_H1f0. zenon_intro zenon_H24f. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H24f). zenon_intro zenon_H56. zenon_intro zenon_H250. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H250). zenon_intro zenon_H252. zenon_intro zenon_H251. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H251). zenon_intro zenon_H1d7. zenon_intro zenon_H253. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H253). zenon_intro zenon_Hf8. zenon_intro zenon_H254. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H254). zenon_intro zenon_Hae. zenon_intro zenon_H255. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H255). zenon_intro zenon_Ha3. zenon_intro zenon_H256. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H256). zenon_intro zenon_Hbc. zenon_intro zenon_H257. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H257). zenon_intro zenon_Hac. zenon_intro zenon_H258. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H258). zenon_intro zenon_Hb3. zenon_intro zenon_H259. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H259). zenon_intro zenon_Hd1. zenon_intro zenon_H25a. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H25a). zenon_intro zenon_H156. zenon_intro zenon_H25b. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H25b). zenon_intro zenon_Hc2. zenon_intro zenon_H25c. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H25c). zenon_intro zenon_Hd9. zenon_intro zenon_H25d. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H25d). zenon_intro zenon_H128. zenon_intro zenon_H25e. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H25e). zenon_intro zenon_H10a. zenon_intro zenon_H25f. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H25f). zenon_intro zenon_H89. zenon_intro zenon_H260. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H260). zenon_intro zenon_H175. zenon_intro zenon_H261. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H261). zenon_intro zenon_H17b. zenon_intro zenon_H262. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H262). zenon_intro zenon_H1f5. zenon_intro zenon_H263. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H263). zenon_intro zenon_H167. zenon_intro zenon_H264. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H264). zenon_intro zenon_H16d. zenon_intro zenon_H265. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H265). zenon_intro zenon_H20. zenon_intro zenon_H266. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H266). zenon_intro zenon_He6. zenon_intro zenon_H267. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H267). zenon_intro zenon_H161. zenon_intro zenon_H268. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H268). zenon_intro zenon_H29. zenon_intro zenon_H269. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H269). zenon_intro zenon_H1da. zenon_intro zenon_H26a. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H26a). zenon_intro zenon_H26c. zenon_intro zenon_H26b. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H26b). zenon_intro zenon_H16e. zenon_intro zenon_H26d. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H26d). zenon_intro zenon_H140. zenon_intro zenon_H26e. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H26e). zenon_intro zenon_H97. zenon_intro zenon_H26f. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H26f). zenon_intro zenon_H171. zenon_intro zenon_H270. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H270). zenon_intro zenon_Hce. zenon_intro zenon_H271. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H271). zenon_intro zenon_H30. zenon_intro zenon_H272. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H272). zenon_intro zenon_H107. zenon_intro zenon_H273. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H273). zenon_intro zenon_H209. zenon_intro zenon_H274. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H274). zenon_intro zenon_H1bb. zenon_intro zenon_H275. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H275). zenon_intro zenon_H15e. zenon_intro zenon_H276. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H276). zenon_intro zenon_H164. zenon_intro zenon_H277. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H277). zenon_intro zenon_He1. zenon_intro zenon_Hdc. % 3.86/4.04 apply (zenon_and_s _ _ ax4). zenon_intro zenon_H4a. zenon_intro zenon_H278. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H278). zenon_intro zenon_H61. zenon_intro zenon_H279. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H279). zenon_intro zenon_H9b. zenon_intro zenon_H27a. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H27a). zenon_intro zenon_H50. zenon_intro zenon_H27b. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H27b). zenon_intro zenon_H5c. zenon_intro zenon_H17e. % 3.86/4.04 apply (zenon_and_s _ _ ax5). zenon_intro zenon_H27d. zenon_intro zenon_H27c. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H27c). zenon_intro zenon_H27f. zenon_intro zenon_H27e. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H27e). zenon_intro zenon_H281. zenon_intro zenon_H280. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H27d); [ zenon_intro zenon_H283 | zenon_intro zenon_H282 ]. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H283). zenon_intro zenon_H174. zenon_intro zenon_H284. % 3.86/4.04 exact (zenon_H284 zenon_H174). % 3.86/4.04 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_H286 | zenon_intro zenon_H285 ]. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H286). zenon_intro zenon_H28. zenon_intro zenon_H148. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H27f); [ zenon_intro zenon_H288 | zenon_intro zenon_H287 ]. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H288). zenon_intro zenon_H153. zenon_intro zenon_H18d. % 3.86/4.04 exact (zenon_H148 zenon_H153). % 3.86/4.04 apply (zenon_or_s _ _ zenon_H287); [ zenon_intro zenon_H1d | zenon_intro zenon_H289 ]. % 3.86/4.04 apply (zenon_L1_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H28a | zenon_intro zenon_H20b ]. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H28a). zenon_intro zenon_H31. zenon_intro zenon_H3b. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H16b | zenon_intro zenon_H28b ]. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H16b). zenon_intro zenon_H21. zenon_intro zenon_H16c. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H280); [ zenon_intro zenon_H25 | zenon_intro zenon_H28c ]. % 3.86/4.04 apply (zenon_L3_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H28c); [ zenon_intro zenon_H2e | zenon_intro zenon_H28d ]. % 3.86/4.04 apply (zenon_L5_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H35 | zenon_intro zenon_H37 ]. % 3.86/4.04 apply (zenon_L7_); trivial. % 3.86/4.04 apply (zenon_L8_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_H3a | zenon_intro zenon_H28e ]. % 3.86/4.04 apply (zenon_L9_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_H3e | zenon_intro zenon_H166 ]. % 3.86/4.04 apply (zenon_L10_); trivial. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H166). zenon_intro zenon_H5d. zenon_intro zenon_H91. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H280); [ zenon_intro zenon_H25 | zenon_intro zenon_H28c ]. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H25). zenon_intro zenon_H22. zenon_intro zenon_H26. % 3.86/4.04 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hea ]. % 3.86/4.04 apply (zenon_L11_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H57 | zenon_intro zenon_Heb ]. % 3.86/4.04 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H66 | zenon_intro zenon_Hec ]. % 3.86/4.04 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H48 | zenon_intro zenon_Hef ]. % 3.86/4.04 apply (zenon_L32_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_Hef); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hf0 ]. % 3.86/4.04 apply (zenon_L33_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H98 | zenon_intro zenon_Hc3 ]. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H54 | zenon_intro zenon_H8e ]. % 3.86/4.04 apply (zenon_L16_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H58 | zenon_intro zenon_H8f ]. % 3.86/4.04 apply (zenon_L17_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H5e | zenon_intro zenon_H68 ]. % 3.86/4.04 apply (zenon_L19_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H60 | zenon_intro zenon_H95 ]. % 3.86/4.04 apply (zenon_L20_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H69 | zenon_intro zenon_H96 ]. % 3.86/4.04 apply (zenon_L23_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H32 | zenon_intro zenon_H78 ]. % 3.86/4.04 exact (zenon_H91 zenon_H32). % 3.86/4.04 apply (zenon_L41_); trivial. % 3.86/4.04 apply (zenon_L42_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hed ]. % 3.86/4.04 apply (zenon_L43_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hca ]. % 3.86/4.04 apply (zenon_L40_); trivial. % 3.86/4.04 apply (zenon_L44_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Ha4 | zenon_intro zenon_Hd7 ]. % 3.86/4.04 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H66 | zenon_intro zenon_Hec ]. % 3.86/4.04 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H48 | zenon_intro zenon_Hef ]. % 3.86/4.04 apply (zenon_L48_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_Hef); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hf0 ]. % 3.86/4.04 apply (zenon_L33_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_H98 | zenon_intro zenon_Hc3 ]. % 3.86/4.04 apply (zenon_L55_); trivial. % 3.86/4.04 apply (zenon_L42_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hed ]. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H57 | zenon_intro zenon_H28f ]. % 3.86/4.04 apply (zenon_L43_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_H1f | zenon_intro zenon_H290 ]. % 3.86/4.04 apply (zenon_L56_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H51 | zenon_intro zenon_H58 ]. % 3.86/4.04 apply (zenon_L15_); trivial. % 3.86/4.04 apply (zenon_L58_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hca ]. % 3.86/4.04 apply (zenon_L40_); trivial. % 3.86/4.04 apply (zenon_L44_); trivial. % 3.86/4.04 apply (zenon_L49_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H28c); [ zenon_intro zenon_H2e | zenon_intro zenon_H28d ]. % 3.86/4.04 apply (zenon_L5_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H35 | zenon_intro zenon_H37 ]. % 3.86/4.04 apply (zenon_L59_); trivial. % 3.86/4.04 apply (zenon_L8_); trivial. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H20b). zenon_intro zenon_Hf6. zenon_intro zenon_Hf1. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H16b | zenon_intro zenon_H28b ]. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H16b). zenon_intro zenon_H21. zenon_intro zenon_H16c. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H280); [ zenon_intro zenon_H25 | zenon_intro zenon_H28c ]. % 3.86/4.04 apply (zenon_L3_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H28c); [ zenon_intro zenon_H2e | zenon_intro zenon_H28d ]. % 3.86/4.04 apply (zenon_L60_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H35 | zenon_intro zenon_H37 ]. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H35). zenon_intro zenon_H32. zenon_intro zenon_H36. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H174 | zenon_intro zenon_H291 ]. % 3.86/4.04 elim (classic ((op (e0) (e2)) = (op (e0) (e2)))); [ zenon_intro zenon_H168 | zenon_intro zenon_H24 ]. % 3.86/4.04 cut (((op (e0) (e2)) = (op (e0) (e2))) = ((op (e0) (e0)) = (op (e0) (e2)))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H17b. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H168. % 3.86/4.04 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H24]. % 3.86/4.04 cut (((op (e0) (e2)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H17c]. % 3.86/4.04 congruence. % 3.86/4.04 cut (((op (e0) (e2)) = (e0)) = ((op (e0) (e2)) = (op (e0) (e0)))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H17c. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H21. % 3.86/4.04 cut (((e0) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H178]. % 3.86/4.04 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H24]. % 3.86/4.04 congruence. % 3.86/4.04 apply zenon_H24. apply refl_equal. % 3.86/4.04 apply zenon_H178. apply sym_equal. exact zenon_H174. % 3.86/4.04 apply zenon_H24. apply refl_equal. % 3.86/4.04 apply zenon_H24. apply refl_equal. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H291); [ zenon_intro zenon_Hf2 | zenon_intro zenon_H292 ]. % 3.86/4.04 apply (zenon_L61_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H292); [ zenon_intro zenon_H48 | zenon_intro zenon_H15f ]. % 3.86/4.04 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hea ]. % 3.86/4.04 apply (zenon_L11_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H57 | zenon_intro zenon_Heb ]. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14c ]. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H14d ]. % 3.86/4.04 apply (zenon_L62_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H14e ]. % 3.86/4.04 apply (zenon_L63_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H12c ]. % 3.86/4.04 apply (zenon_L106_); trivial. % 3.86/4.04 apply (zenon_L86_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H139 | zenon_intro zenon_H14f ]. % 3.86/4.04 apply (zenon_L107_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_Haf | zenon_intro zenon_H60 ]. % 3.86/4.04 apply (zenon_L97_); trivial. % 3.86/4.04 apply (zenon_L98_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Ha4 | zenon_intro zenon_Hd7 ]. % 3.86/4.04 apply (zenon_L108_); trivial. % 3.86/4.04 apply (zenon_L99_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hea ]. % 3.86/4.04 apply (zenon_L11_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H57 | zenon_intro zenon_Heb ]. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14c ]. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H22 | zenon_intro zenon_H126 ]. % 3.86/4.04 apply (zenon_L2_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H10b | zenon_intro zenon_H127 ]. % 3.86/4.04 apply (zenon_L113_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hda ]. % 3.86/4.04 apply (zenon_L78_); trivial. % 3.86/4.04 apply (zenon_L109_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H139 | zenon_intro zenon_H14f ]. % 3.86/4.04 apply (zenon_L107_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_Haf | zenon_intro zenon_H60 ]. % 3.86/4.04 apply (zenon_L97_); trivial. % 3.86/4.04 apply (zenon_L98_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Ha4 | zenon_intro zenon_Hd7 ]. % 3.86/4.04 apply (zenon_L108_); trivial. % 3.86/4.04 apply (zenon_L110_); trivial. % 3.86/4.04 apply (zenon_L8_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_H3a | zenon_intro zenon_H28e ]. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H3d. zenon_intro zenon_H3c. % 3.86/4.04 apply (zenon_L114_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_H3e | zenon_intro zenon_H166 ]. % 3.86/4.04 apply (zenon_L10_); trivial. % 3.86/4.04 apply (zenon_L116_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H294 | zenon_intro zenon_H293 ]. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H294). zenon_intro zenon_H170. zenon_intro zenon_H1de. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H27f); [ zenon_intro zenon_H288 | zenon_intro zenon_H287 ]. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H288). zenon_intro zenon_H153. zenon_intro zenon_H18d. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H16b | zenon_intro zenon_H28b ]. % 3.86/4.04 apply (zenon_L118_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_H3a | zenon_intro zenon_H28e ]. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H3d. zenon_intro zenon_H3c. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H280); [ zenon_intro zenon_H25 | zenon_intro zenon_H28c ]. % 3.86/4.04 apply (zenon_L120_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H28c); [ zenon_intro zenon_H2e | zenon_intro zenon_H28d ]. % 3.86/4.04 apply (zenon_L122_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H35 | zenon_intro zenon_H37 ]. % 3.86/4.04 apply (zenon_L124_); trivial. % 3.86/4.04 apply (zenon_L8_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_H3e | zenon_intro zenon_H166 ]. % 3.86/4.04 apply (zenon_L10_); trivial. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H166). zenon_intro zenon_H5d. zenon_intro zenon_H91. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H280); [ zenon_intro zenon_H25 | zenon_intro zenon_H28c ]. % 3.86/4.04 apply (zenon_L120_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H28c); [ zenon_intro zenon_H2e | zenon_intro zenon_H28d ]. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H27. zenon_intro zenon_H2f. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H174 | zenon_intro zenon_H291 ]. % 3.86/4.04 apply (zenon_L125_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H291); [ zenon_intro zenon_Hf2 | zenon_intro zenon_H292 ]. % 3.86/4.04 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hea ]. % 3.86/4.04 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H66 | zenon_intro zenon_Hec ]. % 3.86/4.04 apply (zenon_L126_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hed ]. % 3.86/4.04 apply (zenon_L127_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hca ]. % 3.86/4.04 apply (zenon_L40_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H66 | zenon_intro zenon_H18f ]. % 3.86/4.04 apply (zenon_L153_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H179 | zenon_intro zenon_H190 ]. % 3.86/4.04 apply (zenon_L135_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H187 ]. % 3.86/4.04 apply (zenon_L136_); trivial. % 3.86/4.04 apply (zenon_L154_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H57 | zenon_intro zenon_Heb ]. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H41 | zenon_intro zenon_H191 ]. % 3.86/4.04 apply (zenon_L138_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_H28 | zenon_intro zenon_H192 ]. % 3.86/4.04 exact (zenon_H18d zenon_H28). % 3.86/4.04 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H49 | zenon_intro zenon_H54 ]. % 3.86/4.04 apply (zenon_L139_); trivial. % 3.86/4.04 apply (zenon_L159_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Ha4 | zenon_intro zenon_Hd7 ]. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H41 | zenon_intro zenon_H191 ]. % 3.86/4.04 apply (zenon_L129_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_H28 | zenon_intro zenon_H192 ]. % 3.86/4.04 exact (zenon_H18d zenon_H28). % 3.86/4.04 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H49 | zenon_intro zenon_H54 ]. % 3.86/4.04 apply (zenon_L139_); trivial. % 3.86/4.04 apply (zenon_L159_); trivial. % 3.86/4.04 apply (zenon_L141_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H292); [ zenon_intro zenon_H48 | zenon_intro zenon_H15f ]. % 3.86/4.04 apply (zenon_L160_); trivial. % 3.86/4.04 apply (zenon_L142_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H35 | zenon_intro zenon_H37 ]. % 3.86/4.04 apply (zenon_L124_); trivial. % 3.86/4.04 apply (zenon_L8_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H287); [ zenon_intro zenon_H1d | zenon_intro zenon_H289 ]. % 3.86/4.04 apply (zenon_L1_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H28a | zenon_intro zenon_H20b ]. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H28a). zenon_intro zenon_H31. zenon_intro zenon_H3b. % 3.86/4.04 cut (((op (e2) (e0)) = (e2)) = ((op (e2) (e0)) = (op (e2) (e1)))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H140. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H170. % 3.86/4.04 cut (((e2) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H295]. % 3.86/4.04 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 3.86/4.04 congruence. % 3.86/4.04 apply zenon_H9a. apply refl_equal. % 3.86/4.04 apply zenon_H295. apply sym_equal. exact zenon_H31. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H20b). zenon_intro zenon_Hf6. zenon_intro zenon_Hf1. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H16b | zenon_intro zenon_H28b ]. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H16b). zenon_intro zenon_H21. zenon_intro zenon_H16c. % 3.86/4.04 exact (zenon_H1de zenon_H21). % 3.86/4.04 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_H3a | zenon_intro zenon_H28e ]. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H3d. zenon_intro zenon_H3c. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H280); [ zenon_intro zenon_H25 | zenon_intro zenon_H28c ]. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H25). zenon_intro zenon_H22. zenon_intro zenon_H26. % 3.86/4.04 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hea ]. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14c ]. % 3.86/4.04 apply (zenon_L161_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H139 | zenon_intro zenon_H14f ]. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H21d); [ zenon_intro zenon_H15f | zenon_intro zenon_H296 ]. % 3.86/4.04 apply (zenon_L173_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H54 | zenon_intro zenon_H297 ]. % 3.86/4.04 cut (((op (e0) (e0)) = (e1)) = ((op (e0) (e0)) = (op (e3) (e0)))). % 3.86/4.04 intro zenon_D_pnotp. % 3.86/4.04 apply zenon_H1eb. % 3.86/4.04 rewrite <- zenon_D_pnotp. % 3.86/4.04 exact zenon_H41. % 3.86/4.04 cut (((e1) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H55]. % 3.86/4.04 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H207]. % 3.86/4.04 congruence. % 3.86/4.04 apply zenon_H207. apply refl_equal. % 3.86/4.04 apply zenon_H55. apply sym_equal. exact zenon_H54. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_H1e0 | zenon_intro zenon_H187 ]. % 3.86/4.04 apply (zenon_L174_); trivial. % 3.86/4.04 exact (zenon_H26 zenon_H187). % 3.86/4.04 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_Haf | zenon_intro zenon_H60 ]. % 3.86/4.04 apply (zenon_L183_); trivial. % 3.86/4.04 apply (zenon_L20_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H57 | zenon_intro zenon_Heb ]. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Hfe | zenon_intro zenon_H14c ]. % 3.86/4.04 apply (zenon_L161_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H139 | zenon_intro zenon_H14f ]. % 3.86/4.04 apply (zenon_L107_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_Haf | zenon_intro zenon_H60 ]. % 3.86/4.04 apply (zenon_L183_); trivial. % 3.86/4.04 apply (zenon_L20_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Ha4 | zenon_intro zenon_Hd7 ]. % 3.86/4.04 apply (zenon_L164_); trivial. % 3.86/4.04 apply (zenon_L49_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H28c); [ zenon_intro zenon_H2e | zenon_intro zenon_H28d ]. % 3.86/4.04 apply (zenon_L122_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H35 | zenon_intro zenon_H37 ]. % 3.86/4.04 apply (zenon_L124_); trivial. % 3.86/4.04 apply (zenon_L8_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_H3e | zenon_intro zenon_H166 ]. % 3.86/4.04 apply (zenon_L10_); trivial. % 3.86/4.04 apply (zenon_L116_); trivial. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H293). zenon_intro zenon_H187. zenon_intro zenon_H1ea. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H27f); [ zenon_intro zenon_H288 | zenon_intro zenon_H287 ]. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H288). zenon_intro zenon_H153. zenon_intro zenon_H18d. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H16b | zenon_intro zenon_H28b ]. % 3.86/4.04 apply (zenon_L118_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_H3a | zenon_intro zenon_H28e ]. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H3d. zenon_intro zenon_H3c. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H280); [ zenon_intro zenon_H25 | zenon_intro zenon_H28c ]. % 3.86/4.04 apply (zenon_L184_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H28c); [ zenon_intro zenon_H2e | zenon_intro zenon_H28d ]. % 3.86/4.04 apply (zenon_L122_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H35 | zenon_intro zenon_H37 ]. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H35). zenon_intro zenon_H32. zenon_intro zenon_H36. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H174 | zenon_intro zenon_H291 ]. % 3.86/4.04 apply (zenon_L125_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H291); [ zenon_intro zenon_Hf2 | zenon_intro zenon_H292 ]. % 3.86/4.04 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H66 | zenon_intro zenon_Hec ]. % 3.86/4.04 apply (zenon_L185_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hed ]. % 3.86/4.04 apply (zenon_L127_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hca ]. % 3.86/4.04 apply (zenon_L190_); trivial. % 3.86/4.04 apply (zenon_L193_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H292); [ zenon_intro zenon_H48 | zenon_intro zenon_H15f ]. % 3.86/4.04 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He4 ]. % 3.86/4.04 apply (zenon_L195_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_H27 | zenon_intro zenon_He5 ]. % 3.86/4.04 apply (zenon_L121_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_H8a | zenon_intro zenon_H68 ]. % 3.86/4.04 apply (zenon_L100_); trivial. % 3.86/4.04 apply (zenon_L202_); trivial. % 3.86/4.04 apply (zenon_L137_); trivial. % 3.86/4.04 apply (zenon_L8_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_H3e | zenon_intro zenon_H166 ]. % 3.86/4.04 apply (zenon_L10_); trivial. % 3.86/4.04 apply (zenon_L203_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H287); [ zenon_intro zenon_H1d | zenon_intro zenon_H289 ]. % 3.86/4.04 apply (zenon_L1_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H28a | zenon_intro zenon_H20b ]. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H28a). zenon_intro zenon_H31. zenon_intro zenon_H3b. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H16b | zenon_intro zenon_H28b ]. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H16b). zenon_intro zenon_H21. zenon_intro zenon_H16c. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H280); [ zenon_intro zenon_H25 | zenon_intro zenon_H28c ]. % 3.86/4.04 apply (zenon_L184_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H28c); [ zenon_intro zenon_H2e | zenon_intro zenon_H28d ]. % 3.86/4.04 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H27. zenon_intro zenon_H2f. % 3.86/4.04 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hea ]. % 3.86/4.04 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H66 | zenon_intro zenon_Hec ]. % 3.86/4.04 apply (zenon_L185_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hed ]. % 3.86/4.04 apply (zenon_L211_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hca ]. % 3.86/4.04 apply (zenon_L64_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H298 ]. % 3.86/4.04 apply (zenon_L211_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H195 | zenon_intro zenon_H299 ]. % 3.86/4.04 apply (zenon_L213_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H299); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hf6 ]. % 3.86/4.04 apply (zenon_L214_); trivial. % 3.86/4.04 exact (zenon_H2f zenon_Hf6). % 3.86/4.04 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H57 | zenon_intro zenon_Heb ]. % 3.86/4.04 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_H66 | zenon_intro zenon_Hec ]. % 3.86/4.04 apply (zenon_L185_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hed ]. % 3.86/4.04 apply (zenon_L43_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hca ]. % 3.86/4.04 apply (zenon_L64_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H298 ]. % 3.86/4.04 apply (zenon_L43_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H195 | zenon_intro zenon_H299 ]. % 3.86/4.04 apply (zenon_L216_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H299); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hf6 ]. % 3.86/4.04 apply (zenon_L214_); trivial. % 3.86/4.04 exact (zenon_H2f zenon_Hf6). % 3.86/4.04 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Ha4 | zenon_intro zenon_Hd7 ]. % 3.86/4.04 apply (zenon_L108_); trivial. % 3.86/4.04 apply (zenon_L141_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H35 | zenon_intro zenon_H37 ]. % 3.86/4.04 apply (zenon_L7_); trivial. % 3.86/4.04 apply (zenon_L8_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_H3a | zenon_intro zenon_H28e ]. % 3.86/4.04 apply (zenon_L9_); trivial. % 3.86/4.04 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_H3e | zenon_intro zenon_H166 ]. % 3.86/4.04 apply (zenon_L10_); trivial. % 3.86/4.04 apply (zenon_L203_); trivial. % 3.86/4.04 apply (zenon_L218_); trivial. % 3.86/4.04 Qed. % 3.86/4.04 % SZS output end Proof % 3.86/4.04 (* END-PROOF *) % 3.86/4.04 nodes searched: 172344 % 3.86/4.04 max branch formulas: 295 % 3.86/4.04 proof nodes created: 6577 % 3.86/4.04 formulas created: 44058 % 3.86/4.04 %------------------------------------------------------------------------------